Follow the instructions here: http://docs.docker.io/en/master/installation/google/

Assuming the last instruction works:

sudo docker run busybox echo 'docker on GCE \o/'

Run this:

sudo docker run sethladd/docker-dart dart --version

You should see something like:

Pulling repository sethladd/docker-dart
3df1fbb95c1f: Download complete
8dbd9e392a96: Download complete
5581b213d8ed: Download complete
5242b0ef847e: Download complete
33626c0daf8f: Download complete
8b9f8f28678f: Download complete
3696f4eade8a: Download complete
a805a53d4a72: Download complete
Dart VM version: 1.0.0.10_r30798 (Mon Dec 2 10:31:15 2013) on "linux_x64"

You're now running Dart via Docker on Google Compute Cloud.

Cool!

Props to +Brian Dorsey and +Seth Ladd for putting the pieces together.