Last week Senator Arlen Specter introduced a Bill on Stem Cell Research to the Senate. You can watch the specch he made - note that he "sought recognition to introduce" the bill.
The Bill has been given the number S.3766. It has two co-sponsors, the Senators from California Senator Boxer and Senator Feinstein. The Bill was read twice and referred to the Committee on Health, Education, Labor, and Pensions.
The Bill can be read here
The stages in the legislative process are set out in a Senate "flowchart"