Yes, LASIK can correct astigmatism, as well as myopia (shortsightedness) and hyperopia (longsightedness).
It can correct any of these problems fully, within certain limits.
For example, the maximum shortsightedness that can be corrected is around 1000 degrees, depending on corneal thickness. With astigmatism, the maximum is lower, around about 400-450 degrees or so.
Bear in mind that any refractive surgery has a risk of under or over correction, although in most cases, the final result will be very close ie within +/- 50 degrees or so from the target.
