Can I change the color of auto detected links on UITextView?

You can use the UIAppearance protocol to apply changes for all text views:

Swift 4.x+:

UITextView.appearance().linkTextAttributes = [ .foregroundColor: UIColor.red ]

Swift 3.x:

UITextView.appearance().linkTextAttributes = [ NSForegroundColorAttributeName: UIColor.red ]

Swift 2.x:

UITextView.appearance().linkTextAttributes = [ NSForegroundColorAttributeName: UIColor.redColor() ]

Objective-C:

[UITextView appearance].linkTextAttributes = @{ NSForegroundColorAttributeName : UIColor.redColor };

Appearance for UITextView is not documented, but works well.

Keep in mind UIAppearance notes:

iOS applies appearance changes when a view enters a window, it doesn’t change the appearance of a view that’s already in a window. To change the appearance of a view that’s currently in a window, remove the view from the view hierarchy and then put it back.

In other words: Calling this code in init(), or init(coder:) methods will change UI Object appearance, but calling in loadView(), or viewDidLoad() of viewController won't.
If you want to set appearance for whole application, application(_:didFinishLaunchingWithOptions:) is good place for calling such code.

On iOS 7 you can set the tintColor of the UITextView. It affects the link color as well as the cursor line and the selected text color.

iOS 7 also added a new property to UITextView called linkTextAttributes which would appear to let you fully control the link style.