How can I recover deleted text messages from my iPhone?

If you were syncing Messages with iCloud and deleted them, they can't be recovered. If you weren't syncing Messages with iCloud, do you have a backup you can restore from? Restoring from a backup erases all data currently on your device. Any data newer than when the backup was made will be erased. A restore is an all or nothing restore. You can't access a backup and only restore certain files.

Backup - Restore your device from an iCloud or iTunes backup.