Using UIPickerview is the right way to go to implement it according to Apple's Human Interface Guidelines
If you select drop down in mobile safari it will show UIPickerview to let the use choose drop down items.
Alternatively
you can use UIPopoverController till iOS 9 as its deprecated but its better to stick with UIModalPresentationPopover of view you want o show as well
you can use UIActionsheet to show the items but it's better to use UIAlertViewController and choose UIActionSheetstyle to show as the former is deprecated in latest versions