The Kerr effect is present in many different transparent media, but not in vacuum. You're probably right that sufficient power density would give rise to self-focusing by gravitational lensing, but it seems like the necessary power density would be very high — the gravitational acceleration needs to be a substantial fraction of c very frequently, like 0.001c over every interval where diffraction gives you a divergence of one milliradian. A narrower beam moves the escaping light you need to capture closer to the center of mass of the beam, but also increases that divergence.

It isn't obvious to me how to calculate this. Can anyone help?