Can very high power laser beams self-focus in vacuum? I first recall reading about such an effect in a SF story entitled "Rails Across the Galaxy" which involved self focusing laser beams. And in a science paper here.
 A: From your link's abstract:

We argue that long-range photon-photon attraction induced by the dipole interaction of two electron-positron loops can lead to “vacuum self-focusing” of very intense laser beams. The focusing angle θF is found to increase with the beam intensity I as θF∼I^4∕3; for the laser beams available at present or in the near future, θF≃10^−10 - 10^−7.

This is a very small angle, practically non measurable as they say in their conclusion:

Our calculation shows that the focussing effect is present even for the plane wave, for
which the leading order contribution from the box diagram of Fig. 1(a) vanishes. The
magnitude of the expected effect however makes its experimental observation challenging.
In particular, in a realistic experimental setup it would have to be distinguished from the
non–linear effects caused by the presence of the air.

Even in vacuum observing such small focusing  will be hard, let alone using it for some purpose, imo.
A: Well if the experiment was performed in space the observation of such small focusing angles wouldn’t be very difficult. One would simply need to allow the beam a longer distance to propagate so as to see the effect. 
As for the angle being much less than the divergence of a “typical” laser beam this is merely a function of beam diameter. If (as proposed by Philip Lubin at UC Santa Barbra) an ordered array of phased lasers were constructed in space up to a few kilometers in diameter or so then the divergence angle of a beam such as that would be sufficiently small that the effect could perhaps be observed. .... Which of course does in fact open the door to at least the theoretical possibility of long distance divergenceless laser beam propagation in vacuum and thus power beaming over interstellar distances.  
