Can I put any song I've written on Pretzel?

That depends. Do you own it?

To have a song go into the Pretzel catalog, the artist or rights holder must own the Master and the Publishing of that song. We sync license every song in our catalog and a sync license needs permission from both the master recording (usually owned by the record label) and the composition (usually owned by a publishing company).

Now you could own both of these yourself if you are an independent artist. 

As long as you own, or get the people who own your assets involved in the agreement process, your music can be on Pretzel.