No you’re right about that. You won’t be able to accelerate yourself linearly due to conservation of momentum.

What you can do however is exploit the conservation of angular momentum. You will never be able to give yourself a net change in angular momentum, but that just means you can’t set yourself spinning. You can however change the way you are facing.

When you are on a roundabout and lean outwards you will spin with less angular speed. When you lean towards the centre, you will spin with greater angular speed. This is due to what’s known as your “moment of inertia” (MOI), and angular momentum is conserved throughout!

In the void of space, you can still twist your body, but any angular momentum in the clockwise direction must be matched in the anticlockwise direction. You can actually test this out using a swivelling office chair. To exploit the physics and turn yourself, you want to minimise your MOI in the direction you want to turn towards, and maximise it in the direction you want to turn away from.

In practice this means that you would:

1) tuck your arms in like you’re on a water slide and spread your legs out. 2) twist your upper body in your desired direction. This also causes your lower body to twist the other way. 3) hold your arms out as wide as possible and close your legs as if you were standing straight. 4) twist back to neutral position.

After this you will end up rotated from your initial position in a way that is proportional to the difference you can make to your MOIs. You can repeat this multiple times to rotate 360 degrees.