Can I restore my deleted texts messages?

Do you have iCloud set to sync your messages to other devices? (not your backup to iCloud, but iCloud's Messaging feature). In iCloud settings, if Messages is turned ON then that means that your messages are not part of your iPhone's backup and cannot be recovered.

If this feature is OFF, then restore your last backup (provided that a backup was not performed after the message was deleted). Note that restoring is all or nothing, and anything that occurred since the last backup will not get restored (aside from things saved in iCloud or other cloud services).