I think now that i understand what the author of original post means to do,so please comment if i understood you correctly.
Plan is to enter masters in math,try to get better GPA and then submit using only his new master diploma for PhD. If that is your intention,yes,that could work. As far as i know,masters program in USA lasts for one year. If you have time,will and funds to do it,sure,go ahead. You can get higher GPA and MSc in mathematics while learning something new in process.
Other advice is to get your current GPA transcribed to european grade standard. Go to the websites of the universities where you intend to apply for PhD program and see if you meet minimum grade needed. Since there isn't universal grade minimum, you may find out that you qualify in one of them with your current GPA. Remember,GPA is not be all end all criteria. Personal experience,minimum grade average was 3.5 (very good). When i applied they checked my grade average to see if i meet their minimum and they never looked at it again. It was mostly administrative criteria. Interviews had much more weight in their decision to admit me to PhD program.
Hope it helps