Since Aseprite v1.2-beta10 you can add/remove extensions to/from Aseprite. Extensions are distributed as .zip files and you can manage them from Edit > Preferences > Extensions:

Extensions in Preferences

Add/Remove Extensions

In Edit > Preferences > Extensions there is a "Add Extension" button. You can use it to select a .zip file with an extension. The extension will uncompressed in your configuration directory inside a extensions subfolder.

Extension Content

The content inside the .zip file varies depending of the kind of extension but they must contain one file inside: