How to create vCard/vcf file to use in share sheet?

You may use a CNContact (requires iOS 9):

let contact = CNMutableContact()
    contact.givenName = "John"
    contact.familyName = "Doe"
    contact.emailAddresses = [
      CNLabeledValue(label: CNLabelWork, value: "[email protected]")
    ]

The trick here is to save the contact to a VCard (.vcf) file using CNContactVCardSerialization.dataWithContacts, then pass the file URL to the UIActivityViewController. The activity view controller detects the VCard format from the file extension, and shows the apps where the format is supported (e.g. Messages, Mail, Notes, Airdrop, etc)

Example:

@IBAction func buttonTapped(button: UIButton) {

    let contact = createContact()

    do {
        try shareContacts([contact])
    }
    catch {
        // Handle error
    }
}

func shareContacts(contacts: [CNContact]) throws {

    guard let directoryURL = NSFileManager.defaultManager().URLsForDirectory(.CachesDirectory, inDomains: .UserDomainMask).first else {
        return
    }

    var filename = NSUUID().UUIDString

    // Create a human friendly file name if sharing a single contact.
    if let contact = contacts.first where contacts.count == 1 {

        if let fullname = CNContactFormatter().stringFromContact(contact) {
            filename = fullname.componentsSeparatedByString(" ").joinWithSeparator("")
        }
    }

    let fileURL = directoryURL
        .URLByAppendingPathComponent(filename)
        .URLByAppendingPathExtension("vcf")

    let data = try CNContactVCardSerialization.dataWithContacts(contacts)

    print("filename: \(filename)")
    print("contact: \(String(data: data, encoding: NSUTF8StringEncoding))")

    try data.writeToURL(fileURL, options: [.AtomicWrite])

    let activityViewController = UIActivityViewController(
        activityItems: [fileURL],
        applicationActivities: nil
    )

    presentViewController(activityViewController, animated: true, completion: {})
}

func createContact() -> CNContact {

    // Creating a mutable object to add to the contact
    let contact = CNMutableContact()

    contact.imageData = NSData() // The profile picture as a NSData object

    contact.givenName = "John"
    contact.familyName = "Appleseed"

    let homeEmail = CNLabeledValue(label:CNLabelHome, value:"[email protected]")
    let workEmail = CNLabeledValue(label:CNLabelWork, value:"[email protected]")
    contact.emailAddresses = [homeEmail, workEmail]

    contact.phoneNumbers = [CNLabeledValue(
        label:CNLabelPhoneNumberiPhone,
        value:CNPhoneNumber(stringValue:"(408) 555-0126"))]

    return contact
}

It is very simple to create contact from your iOS app and share over the external apps.

First you need to create Share Button Action like below :-

-(void)shareContactAction:(UIButton*)sender
{  
    CNMutableContact *selectedCon = [[CNMutableContact alloc] init];
    selectedCon.givenName = @"ABC";
    selectedCon.familyName = @"XYZ";
    NSString *phoneNum = @"+91-XXXXXXXXXXX"
    CNLabeledValue *contactNum1 = [CNLabeledValue labeledValueWithLabel:CNLabelHome value:[CNPhoneNumber phoneNumberWithStringValue:phoneNum]];
    selectedCon.phoneNumbers = @[contactNum1];
    NSString *url=[self saveContactDetailsToDocDir:selectedCon];
    UIActivityViewController *activityViewController = [[UIActivityViewController alloc] initWithActivityItems:@[@"Contact", [NSURL fileURLWithPath:url]] applicationActivities:nil];
    [self presentViewController:activityViewController animated:YES completion:nil];     
}

Than you can call the function below which will return the path of the contact card in above button event.

- (NSString *)saveContactDetailsToDocDir:(CNContact *)contact {

    NSArray *paths = NSSearchPathForDirectoriesInDomains (NSDocumentDirectory,     NSUserDomainMask, YES);
    NSString *documentsDirectory = [paths objectAtIndex:0];
    NSString * contactCardPath = [documentsDirectory stringByAppendingString:@"/vCardName.vcf"];
    NSArray *array = [[NSArray alloc] initWithObjects:contact, nil];
    NSError *error;
    NSData *data = [CNContactVCardSerialization dataWithContacts:array error:&error];
    [data writeToFile:contactCardPath atomically:YES];

    return contactCardPath;
}