How to check if the user gave permission to use the camera?

Swift 3.0 Updated Solution

func callCamera(){
    let myPickerController = UIImagePickerController()
    myPickerController.delegate = self;
    myPickerController.sourceType = UIImagePickerControllerSourceType.camera

    self.present(myPickerController, animated: true, completion: nil)
    NSLog("Camera");
}
func checkCamera() {
    let authStatus = AVCaptureDevice.authorizationStatus(forMediaType: AVMediaTypeVideo)
    switch authStatus {
    case .authorized: callCamera() // Do your stuff here i.e. callCameraMethod()
    case .denied: alertPromptToAllowCameraAccessViaSetting()
    case .notDetermined: alertToEncourageCameraAccessInitially()
    default: alertToEncourageCameraAccessInitially()
    }
}

func alertToEncourageCameraAccessInitially() {
    let alert = UIAlertController(
        title: "IMPORTANT",
        message: "Camera access required for capturing photos!",
        preferredStyle: UIAlertControllerStyle.alert
    )
    alert.addAction(UIAlertAction(title: "Cancel", style: .default, handler: nil))
    alert.addAction(UIAlertAction(title: "Allow Camera", style: .cancel, handler: { (alert) -> Void in
        UIApplication.shared.openURL(URL(string: UIApplicationOpenSettingsURLString)!)
    }))
    present(alert, animated: true, completion: nil)
}

func alertPromptToAllowCameraAccessViaSetting() {

    let alert = UIAlertController(
        title: "IMPORTANT",
        message: "Camera access required for capturing photos!",
        preferredStyle: UIAlertControllerStyle.alert
    )
    alert.addAction(UIAlertAction(title: "Dismiss", style: .cancel) { alert in
        if AVCaptureDevice.devices(withMediaType: AVMediaTypeVideo).count > 0 {
            AVCaptureDevice.requestAccess(forMediaType: AVMediaTypeVideo) { granted in
                DispatchQueue.main.async() {
                    self.checkCamera() } }
        }
        }
    )
    present(alert, animated: true, completion: nil)
}

You can use the following code for doing the same:

if AVCaptureDevice.authorizationStatusForMediaType(AVMediaTypeVideo) ==  AVAuthorizationStatus.Authorized {
    // Already Authorized
} else {
    AVCaptureDevice.requestAccessForMediaType(AVMediaTypeVideo, completionHandler: { (granted: Bool) -> Void in
       if granted == true {
           // User granted
       } else {
           // User rejected
       }
   })
}

NOTE:

1. Make sure that you add the AVFoundation Framework in the Link Binary section of build phases
2. You should write import AVFoundation on your class for importing AVFoundation

SWIFT 3

if AVCaptureDevice.authorizationStatus(forMediaType: AVMediaTypeVideo) ==  AVAuthorizationStatus.authorized {
   // Already Authorized
} else {
   AVCaptureDevice.requestAccess(forMediaType: AVMediaTypeVideo, completionHandler: { (granted: Bool) -> Void in
      if granted == true {
         // User granted
      } else {
         // User Rejected
      }
   })
}

Swift 4

if AVCaptureDevice.authorizationStatus(for: .video) ==  .authorized {
    //already authorized
} else {
    AVCaptureDevice.requestAccess(for: .video, completionHandler: { (granted: Bool) in
        if granted {
            //access allowed
        } else {
            //access denied
        }
    })
}

The following is a cleaned up answer updated for Swift 4.x:

Starting with iOS 10, you must also request permission in the info.plist file to avoid a crash:

Privacy - Camera Usage Description

You must provide a string that is presented to the user with this key. Failure to do so will result in a crash when attempting to access the camera.

import AVFoundation

func checkCameraAccess() {
    switch AVCaptureDevice.authorizationStatus(for: .video) {
    case .denied:
        print("Denied, request permission from settings")
        presentCameraSettings()
    case .restricted:
        print("Restricted, device owner must approve")
    case .authorized:
        print("Authorized, proceed")
    case .notDetermined:
        AVCaptureDevice.requestAccess(for: .video) { success in
            if success {
                print("Permission granted, proceed")
            } else {
                print("Permission denied")
            }
        }
    }
}

func presentCameraSettings() {
    let alertController = UIAlertController(title: "Error",
                                  message: "Camera access is denied",
                                  preferredStyle: .alert)
    alertController.addAction(UIAlertAction(title: "Cancel", style: .default))
    alertController.addAction(UIAlertAction(title: "Settings", style: .cancel) { _ in
        if let url = URL(string: UIApplicationOpenSettingsURLString) {
            UIApplication.shared.open(url, options: [:], completionHandler: { _ in
                // Handle
            })
        }
    })

    present(alertController, animated: true)
}

This will test for the four possible answers, and then either request permission if it is notDetermined, or direct the user to settings to enable it if it is denied. If it is restricted, the current user may not be able to enable it, but you should provide some form of guidance to them.

This will open the camera when permission is given by the user. Otherwise show alert for asking permission.

func openCamera(){
        
        let authStatus = AVCaptureDevice.authorizationStatus(for: AVMediaType.video)
        
        switch (authStatus){
            
        case .notDetermined, .restricted, .denied:
            showAlert(title: "Unable to access the Camera", message: "To enable access, go to Settings > Privacy > Camera and turn on Camera access for this app.")
        case .authorized:
            alert.dismiss(animated: true, completion: nil)
            if(UIImagePickerController .isSourceTypeAvailable(.camera)){
                picker.sourceType = .camera
                picker.showsCameraControls=true
                picker.allowsEditing=true
                self.viewController!.present(picker, animated: true, completion: nil)
            }
        }
}

after this call this function for showing alert

func showAlert(title:String, message:String) {
        let alert = UIAlertController(title: title,
                                      message: message,
                                      preferredStyle: UIAlertController.Style.alert)
        
        let okAction = UIAlertAction(title: "OK", style: .cancel, handler: nil)
        alert.addAction(okAction)
        
        let settingsAction = UIAlertAction(title: "Settings", style: .default, handler: { _ in
            // Take the user to Settings app to possibly change permission.
            guard let settingsUrl = URL(string: UIApplication.openSettingsURLString) else { return }
            if UIApplication.shared.canOpenURL(settingsUrl) {
                if #available(iOS 10.0, *) {
                    UIApplication.shared.open(settingsUrl, completionHandler: { (success) in
                        // Finished opening URL
                    })
                } else {
                    // Fallback on earlier versions
                    UIApplication.shared.openURL(settingsUrl)
                }
            }
        })
        alert.addAction(settingsAction)
        
        self.viewController!.present(alert, animated: true, completion: nil)
    }