The bill does not make exceptions for any fetal anomalies.
Many states have bans at 20 weeks, but none have successfully passed a 12-week ban.
Governor Beebe says this particular bill appears to be unconstitutional.
At age 22, Ali Taylor found herself young and pregnant.
"I was struggling in my life at that point. I really wasn't taking care of myself or people in my life," said Taylor. "So I decided to terminate the pregnancy, and I did."
Now 16 years later, she has no regrets about her choice and says the fact lawmakers are choosing right now, whether to effectively make abortions illegal in Arkansas is frightening.
"It scares me for Arkansas women," said Taylor.
Senator Jason Rapert is sponsoring the bill and says the measure is constitutional.