Sure you can. In both cases (earth or space), this works because of conservation of angular momentum.
Most folks intuitively understand conservation of linear momentum: if you’re floating in the middle of the ISS, and you shove a bowling ball in one direction, your body will move in the other direction. The bowling ball and your body, considered as a single mass, have a fixed location in the ISS; that’s true before and after you shove the ball away.
Angular momentum can be thought of in an analogous way. If you’re floating in the middle of the ISS, all of your matter has a fixed total angular momentum. If you start moving your arms in a circle, you are giving them angular momentum in one direction of rotation, and the rest of your body will develop angular momentum in the opposite direction of rotation. Stop moving your arms in that circle, and the rest of your body will stop rotating in the opposite direction. The entire time, your arms and the rest of your body, considered as a single mass, will have the same total angular momentum as when you started.
Somewhere out there is a video of Skylab astronauts demonstrating a version of the above exercise. IIRC, there were two astronauts floating stationary side by side, both facing the camera as if standing at attention. On cue, the both start flailing their arms in a “stirring the cauldron” kind of motion, and do something similar with their legs. They both begin to rotate left on a head-to-toes axis; once they’ve turned 90 degrees to their left, they stop flailing, and their rotation stops. On cue, they start again, and stop when they’re facing away from the camera. A couple more cycles of this, and they’re facing the camera again. I’ve looked for this on YouTube, but can’t find it. Maybe someone else can?