Border around UITextView

 #import <QuartzCore/QuartzCore.h> 

Import the above framework and include these lines in your class where textview is defined.

[[self.textview layer] setBorderColor:[[UIColor grayColor] CGColor]];
[[self.textview layer] setBorderWidth:2.3];
[[self.textview layer] setCornerRadius:15];

Swift solution.

self.textview.layer.borderColor = UIColor.gray.cgColor              
self.textview.layer.borderWidth = 2.3                
self.textview.layer.cornerRadius = 15