Can I mix acrylic paints into resin?
Yes, you can mix acrylic paint into resin (I assume you mean epoxy resin), but the results may wary from paint to paint.
The general rules apply:

You can mix wet ingredients (paints, inks) up to 10% of the volume of resin into it. Anything more makes the resin cloudy or not cure correctly. Better be safe and limit it to 5%.
If possible, mix the wet ingredients into the hardener before mixing the hardener and resin together. That guarantees even mixing and doesn't shorten your working time.

I strongly advice against using cheap acrylic paints, because they contain less pigments and more water than high quality paints, and sometimes additives like chalk. That means they make the resin opaque and you need more paint to reach the desired color of resin, which leads us back to problem 1: your resin could become cloudy.
I've had a bad experience with transparent glass color, probably because it wasn't acrylic based. The color didn't mix with the epoxy at all and formed little flakes of color in the otherwise untinted resin instead. Have a look at the result here.
I've had good experiences with acrylic colors and food colors. Both tend to mix well with resin, but both can change color quite drastically. Have a look at my results here.

Some food colors changed the physical properties of the resin and made it goopy
Some food colors didn't mix well with the resin
All food colors changed color in the resin
Food colors are not light stable! They will fade when exposed to light
All acrylics mixed well with the resin
Some acrylics changed color in the resin quite drastically, others not at all. I assume you'll face color changes especially with red paints because red pigments are known to be less stable than most other pigments.
Some acrylics are less light stable than others and will slowly fade when exposed to light. The amount of light stability is usually printed as a symbol on the tube of paint (at least on high quality paints).

I've had the least problems at all with powders like cheap eye shadow. It makes the resin opaque, but often adds a shimmer or pearlescent effect and in my experience never changed color in the resin. Be aware that powders sink to the bottom of the mould, which might look odd...