After a few days of floating around in space, astronauts do actually begin to grow taller.

What actually takes place cannot really be described as, "growing" though.

But in the end, they are taller.

The astronauts grow because there is no gravity in space.  Without any gravity, the spine of the astronaut does not end up carrying the weight of their bodies.  Without the weight on their spine, the spine is able to extend itself.

The growth does not last long however.  Once the astronauts return to Earth, it only takes a week or two for them to shrink back to their original pre-space heights.