Yes, you can put podcasts on your Apple Watch. Here's how you can do it:

1. Open the Apple Watch app on your iPhone.
2. Scroll down and tap on 'Podcasts'.
3. Here you will see a couple of options. 'Listen Now' will automatically sync the shows you listen to most frequently. You can also choose 'Custom' to select the shows you want to sync.
4. Episodes will automatically sync to your Apple Watch when it's charging.
5. Once the episodes are synced, you can listen to them on your Apple Watch without your iPhone.

Remember, you will need a pair of Bluetooth headphones or a speaker to listen to the podcasts on your Apple Watch as it doesn't have a built-in speaker for this purpose.