This article that it is possible:
His situation seems hopeless. However, he remembers the lessons he received as rookie astronaut on swimming in empty space. By applying a weird degenerative form of breaststroke the astronaut slowly moves toward the spaceship and makes it safely back before he runs out of oxygen.
Science 20 cites and MIT paper by Jack Wisdom in support of the claim, although the latter makes no mention of astronauts.
My question is: could an astronaut doing a space 'walk' in space move their center of mass by a useful amount (or even a detectable amount) by moving their arms about by taking advantage of relativity?
Background: On this page is this comment (by the user "Skyler") that was upvoted twice:
In fact, you can "swim" in a vacuum, taking advantage of relativity: science20.com/hammock_physicist/swimming_through_empty_space. However, this is a very subtle effect, and takes hours to move a foot or two.
Similar to this question (except for asking whether an astronaut could really make enough headway to save his own life as claimed by Science 20 and Skyler).