You can use iTunes to exit recovery mode.
(1) Connect your iPhone to your computer and run iTunes on your computer.
(2) Select your iPhone from the list of buttons at the top of iTunes, then click the "Restore" button.
(3) Wait for the backup and restore process to complete, then "restore from backup" in iTunes after the phone has been restored.
Read Apple support for more details:
If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support
NOTE: This method will fix iPhone stuck in recovery mode, but will restore the iPhone in the process. This will erase everything on the iPhone, but a backup will be created during the Restore process, allowing you to recover your data.