Have you tried to reset it ? To solve iPhone stuck in recovery mode by pressing the Home button and the Sleep/Wake button on the top the iPhone's case and holding them down together for 10 seconds. The iPhone should then reset itself and return to the locked state.
Hello,
Thank you for your question. Since your iPhone is stuck in a rebooting loop, I recommend attempting to Restart or Reset the device, which is detailed in this article from the Apple Support page.
If you have any further questions, feel free to post them below.
Thank you,
-John-Paul