From looking at the Podcasts app, you might think that you can’t subscribe to podcasts outside Apple’s iTunes Store. In fact, you can, but the method for doing so is not intuitive.
When viewing a podcast in the Podcasts app, you’ll see a black bar at the base of the window, with a Search field to the right. Paste a podcast URL into this field and tap Search.
A dialogue box will ask if you want to subscribe to the podcast. Tap Subscribe to add it to your list.