I've been a Data Scientist for about 10 years now and all positions I have seen are full time. You can try and get in full time but sadly there don't seem to be many consulting roles.

Being a data scientist requires a solid understanding of mathematical concepts as well and the interviews tend to be notoriously hard. You might consider going thru a boot camp and graduate from there in 6 months with a certificate. It might help you get you in the door. Salaries are pretty good but like I said, most have to go thru many rounds of interview before getting a job.