What is the LDS Church position on abortion?
The LDS Church is against elective abortion. Please read the linked article to better understand the term "elective".
If I had an abortion, can I still become a Mormon?
Yes, you can.
You may need to discuss this with a local Mormon church leader before being baptized, because they will want to make sure you are clear about the LDS teachings on abortion.
Can Mormons have abortions?
(Well, you can do whatever you want, right? But I guess you mean "will the Mormon church approve"...)
If you participate in an elective abortion as an LDS church member, you may risk losing your membership in the Church.
If a child is born out of wedlock, and marriage is not an option, the Church encourages the placement of the child in a loving home through adoption.