Yes, a woman with no Fallopian tubes can get pregnant by way of IVF (in vitro fertilization). Having no tubes does not translate into not ovulating (i.e. not releasing eggs) unless there is another problem affecting it.
For IVF, her oocytes are collected directly from the ovary through a procedure called ovum pick-up of follicle puncture, and then fertilized at the lab. The resulting embryo or embryos are transferred back to her uterus, so that pregnancy takes place.