The Lomography Petzval Portrait Lens is totally compatible with cameras without a full frame sensor. However, on cameras with a smaller image sensor there will be a crop factor so you so you may notice a lesser effect than with a full frame sensor camera. On a crop-sensor camera, the sensor is smaller; so you effectively get a crop of the image you would have got from a full-frame sensor camera.
Below are views of the Petzval lens when attached to cameras with varying crop factors. Each photo shown here was taken from exactly the same position and using the same camera settings. Underneath the photos are links so you can view each shot in high resolution.