Great news. This feature was planned to be added after Early Access launch, but apparently, it's here already!
Starting with version 0.7.20, it will be possible to upload custom tracks from Track Editor, and subscribed tracks will be downloaded automatically, so you can play them in Quick Race, or iterate the design further in Track Editor.
To upload tracks, in Track Editor click File -> Upload To Workshop;
In race selection view, click Get More Tracks to visit Workshop;
Subscribe the tracks you like;
Subscribed tracks will appear in Quick Race and Track Editor track listings.