How do I get printer ink out of my carpet?

there are several products especially for ink, Carbona stain devils for ink comes to mind

You won't...if it isn't too big an area, simply cut around the spot or spots, and replace this cut section with one the same size out of the same material, glue it to the subfloor and no one should be the wiser...if the carpet had a pattern, you need to match part of the pattern you cut.

milk gets ink out of anything. Let it soak in and watch it disappear. Then follow with a good carpet cleaner to get the milk out. Trust me it works, especially on clothing

Years ago I got black stamp pad ink on the arm of a brand new white blouse. Someone told me to use WASHING SODA NOT BAKING SODA on the stain, and it did come out.

You may have to carefully cut out the stained piece, and pat in a remnant piece of your original carpet

Maybe rubbing alcohol and white paper towel. Blot up as much ink as you can and then put clean paper towel over area. Wet towel with rubbing alcohol. May take several days. Awesome Brand Carpet/Stain remover for The Dollar Store might work as well. I would test a tiny spot first before jumping in on the whole works.