Heroku's stacks generally use a read-only filesystem, and even recent stacks with the new ephemeral filesystem won't persist data among dynos or across dyno restarts. The lack of a writable filesystem with data persistence makes running continuous integration on Heroku a non-starter.
TL;DR: No, you can't.
Heroku's stacks generally use a read-only filesystem, and even recent stacks with the new ephemeral filesystem won't persist data among dynos or across dyno restarts. The lack of a writable filesystem with data persistence makes running continuous integration on Heroku a non-starter.