Imagine that an astronaut during an EVA is cut loose from the space station and falls away from it in a tumbling way. Without any foreign object or air to interact with, could he stop tumbling and spinning and turn around to steadily face towards the space station again? The speed of the spinning can be changed by spreading our or curling up. But could the angular momentum be changed or redirected?
Angular momentum is conserved. Something has to be emitted or absorbed to change the angular momentum. Spin rate can be changed by changing the moments of inertia of the object, as a skater does. But the angular momentum is fixed unless they have a rocket or some other mass they can get rid of, a solar sail (and a lot of time), a way to react against Earth's magnetic field, or if someone throws something at them that they catch. The gravity gradient of Earth can also apply torque against the angular momentum.
They could slow their spin rate quite a bit with two masses on long strings that they play out. If they then let go of the strings, that would emit the angular momentum transferred to the masses. I would keep some of those in my pockets.
Orientation is a different matter. If the astronaut has roughly a zero spin rate, they can change which way they are facing without touching anything. There are videos of this being done on the space station. (I think you can find an example in another answer here somewhere.) Cats do this as well in free fall. You can do this even if you are spinning, but the result is harder to see. The axis of their spin cannot change, since that is set by their angular momentum, but the orientation of the body relative to the spin axis can be changed.
There are only two ways he could do this.
The first is if he has something he can spin within his suit -- kind of like a personal CMG. This would effectively "absorb" the angular momentum. It would probably either have to spin fast or be a significant fraction of the astronaut's mass.
The other is if he can throw something away as a reaction mass to counteract the spin. The astronaut would have to throw the mass fairly precisely to zero out his spin. This would have the (possibly) negative consequence of also imparting a change in linear momentum. Not too difficult if it is a cold-gas thruster. Harder if it is a tennis ball...
An addition to Erik's terrific answer, which is 100% correct, there is an additional theoretical method that the astronaut could use to change his spin and rotation.
I really don't think that a human would come up with this by himself, but if an astronaut were already familiar with the Cat righting reflex then he could theoretically right himself by transferring angular momentum to different appendages and then changing the leverage of the appendage and returning the angular momentum. Basically, this means to extend the legs, twist the body, bring the legs back in, then extend the arms, twist the body, then bring the arms back in. Repeat as necessary.
While Erik and Mark's answers are technically correct, an astronaut might (at least, theoretically) try something risky in an emergency:
If the astronaut had something sharp with which to make a hole in his/her suit, or else the suit has an attachment that could be ripped off, he might be able to use the pressurized air within the suit as a sort of make-shift thruster. Pointed in the right direction (spinward), one could negate some small amount of spin (at the cost of some of the air in the suit, of course). This is something you'd only try if the alternative was certain death, of course...
NASA demonstrated that this can work, 'way back around 1970. If it happens, it must be possible.
For those who don't believe the physics: T.R. Kane and M.P. Scher of Stanford, California, in the International Journal of Solids and Structures: "A Dynamical Explanation of the Falling Cat Phenomenon."
Websearch will turn up photos of astronauts (on trampolines, mostly, rather than free-fall) executing this move.