How does the crop sensor factor in with the lens?

I have a Nikon 35mm lens that I want too use to take portrait shots with. I had read that you are not supposed to use a lens that is less than 50mm because it will distort the face. But since I have a 1.5 crop sensor that makes the lens 75mm; would that get rid of the distortion so I can use the lens with no problem?

Uh, your film 35mm lens would be actually be a 52.5mm lens on a digital.

A 50mm lens is a 50mm lens, no matter which sensor you're using. The difference is the "field of vision." With a 1.5 crop sensor, you get the same field of vision as if you would have used a 75mm lens on a full-frame sensor. But the distortion will be the same.
You're taking the same view, but cropping out the middle part and only looking at that.
Your best bet is to take a few steps back when taking the photo. This will lessen the effect of the distortion of the lens, and you can crop in a little during post production.

On a 35mm film camera or full-frame DSLR a focal length of between 85mm to 105mm is considered an ideal portrait focal length. So a 50mm lens on your camera will have the angle of view of a 75mm lens on a 35mm film camera or full-frame DSLR, thus making it a good choice for portraits.

Your 35mm lens is effectively a normal lens on an APS-C sensor camera… Which means that you'll see very little distortion in portraits or any photographs. The advantage of using a 50mm lens over the 35mm on your camera is that it will compress perspective slightly, flattening facial features, which is flattering to the subject.

FYI 35 x 1.5 = 52.5mm and not 75mm, you'd need a 50mm to act like a 75mm fitted to a full frame camera.

Only the first answer is correct.