The short answer to your question is yes, an EF lens can be used on a crop-sensor (EF-S) Canon camera.
The longer answer is that EF-S lenses are designed for crop-sensor lenses, the ‘s’ denotes a smaller image circle, but it’s otherwise a compatible mount. So, lenses designed for full frame (EF) will also work on your camera.
Going the other way, however, does not work, period. Some of the EF-S lenses protrude into the body and so for full frame cameras that would cause the mirror to come into contact and get damaged, but even if they do not, they can’t be used.