Yesterday Apple released iOS 9.3.1 which includes bug fixes, including the bug that was causing links to crash. To update, go to Settings > General > Software Update to download.
If you are having trouble with web links not working when you tap them on your iOS 9 enabled iPhone or iPad, you’re not alone. Several Apple news websites have reported that there is a wide-spread issue in Apple’s latest update that causes the links to fail.
Apple has stated that they “are aware of this issue, and we will release a fix in a software update soon.”
Unfortunately there is no known workaround for this issue at this time. If this issue is affecting you, the best thing to do is keep checking to see if there is an update available by going to Settings > General > Software Update to make sure that you are up-to-date. Though the issue is not isolated to iOS 9.3, the fix will presumably come in iOS 9.3.1.