How to open twitter page in twitter app from my iphone app?

You are looking for the following url:

twitter:///user?screen_name=PAGE

Note that Twitter is not installed on all devices. You should check the result of openURL method. If it fails, open the page in Safari with regular url.

The following code opens twitter page on twitter app if it is already installed, otherwise opens twitter on safari:

NSURL *twitterURL = [NSURL URLWithString:@"twitter://user?screen_name=username"];
if ([[UIApplication sharedApplication] canOpenURL:twitterURL])
    [[UIApplication sharedApplication] openURL:twitterURL];
else
    [[UIApplication sharedApplication] openURL:[NSURL URLWithString:@"http://www.twitter.com/username"]];

Don't forget to replace 'username' with your name.

This is the full code required in Swift. I am using Swift 4 but i believe it is the same for Swift 3.

let Username =  "YOUR_USERNAME_HERE" 
let appURL = NSURL(string: "twitter:///user?screen_name=\(Username)")!
let webURL = NSURL(string: "https://twitter.com/\(Username)")!
let application = UIApplication.shared
if application.canOpenURL(appURL as URL) {
      application.open(appURL as URL)
    } else {
        // if Twitter app is not installed, open URL inside Safari
        application.open(webURL as URL)
    }

Don't forget to add the Info keys needed to use canOpenURL:

I know its quite a late response to this question and I agree that, Murat's answer is absolutely correct. Simply add a check as follows:

NSURL *urlApp = [NSURL URLWithString: [NSString stringWithFormat:@"%@", @"twitter:///user?screen_name=PAGE]];

if ([[UIApplication sharedApplication] canOpenURL:urlApp]){
        [[UIApplication sharedApplication] openURL:urlApp];
    }

I hope this helps someone. Cheers!! :)