Also, as a tip, don't get involved in one of those content writing mills. Having made the unfortunate mistake of getting suckered into hiring those once, their writers are clearly overworked and underpaid. And don't get me started on the final work product :/
My day job involves digital marketing. I do not have a degree in marketing - my background is English. So, as Lisa said, you don't need a degree in marketing to do content writing. But content writing at my job involves so much more than just writing content; you need to have an understanding of SEO best practices, the target audience you are marketing to, and frankly a good handle on the technical matter you are writing about. I feel like a broken record, but content writing is NOT keyword stuffing. It is about writing meaningful, thoughtful content that people will actually find useful and that hasn't been said by a thousand other people already.
My colleagues' backgrounds range from English to technical writing to business administration to marketing to journalists to <insert many other blanks>.
I'm wondering, though, whether content writing is what you're really after here. What do you want to do?