Writing for magazines is a good way to make a career as a writer. There are magazines that only accept writers from the US or native English speakers, but there are also magazines open to people using English as a second or third language. If you check writing job listings from a newsletter like "Freedom with Writing," you'll see that the only requirement is good language and good writing. Just because you're American or a native speaker doesn't mean you're automatically good at English and writing. Being a native speaker doesn't guarantee writing jobs, you need language and writing skills. Rejections usually happen because of poor language skills or bad writing.