Yes, you can put a sleep timer on Apple Podcasts. Here's how you do it:

1. Open the Apple Podcasts app on your iPhone or iPad.
2. Start playing the podcast you want to listen to.
3. Swipe up on the now playing bar at the bottom of the screen. This will bring up additional options.
4. Scroll down until you see the "Sleep Timer" option.
5. Tap on "Sleep Timer."
6. Select the amount of time you want the podcast to play for before it stops. You can choose between 5 minutes, 10 minutes, 15 minutes, 30 minutes, 45 minutes, 1 hour, or when the current episode ends.

After the selected time, the podcast will stop playing, allowing you to go to sleep without worrying about stopping the podcast manually.