Can travis-ci run docker?
As of August 2015, Travis CI officially supports Docker.
See Using Docker in Builds for usage details.
Sorry, while we currently support Docker as an alternative virtualization platform, we don't directly support running Docker inside of the current setup, at least directly.
However, there are workarounds that could help you there from the fine folks at Docker themselves: https://github.com/jpetazzo/sekexe
In case you have not yet solved the problem yourself, here https://github.com/rocker-org/rocker/blob/56cb59cc262e9d2c02f9e11cfacab65f0b659c5f/.travis.yml#L10-L24 you can find a practical example of the solution suggested above.