Yes, but there's not really a point to it
Assuming we had working portal technology and almost limitless power sources, it's feasible. Some minor calibration issues would exist, notably because the constant acceleration due to gravity would be problematic, problematic in this context meaning 'starting to turn the air to plasma'. The air resistance in between the portal wouldn't really slow it down that much assuming that the portals operate in a close system because that air would be gradually accelerated as well. And if you're using a system open to Earth's atmosphere - well, that seems like of silly and risky given that a gust of wind could blow your projectile off track because the slightest acceleration to one side would mean that the projectile would eventually tumble out of the portal. Not to mention that with normal air resistance, it's not going to be going 'crazy fast', and in fact will be going slower than some guns can fire bullets. Given all that, you would also needs the means to drop said projectile with ludicrous precision in the first place, and honestly, it still wouldn't be as precise as a bullet, because bullets spin. This projectile wouldn't spin, so not much accuracy.
Given all the constraints and risks, conventional guns are just better. And, given that apparently you can just fire a portal to the moon, it's not even useful for building up speeds to launch rockets when you don't even need rockets in the first place.