By "non-native" I assume you mean you are a "foreign national." Are you here on a Visa? If so, what type of Visa (work, visitor, family, etc.). or do you have a Green Card? The basic answer to your question is that anyone may buy real estate in the USA, so long as they are not on a "watch list" of any type. However, the difficulty is obtaining a mortgage to buy that house in the USA. If you want a mortgage then all the questions I initially asked will come into play. Some conventional lenders will make a loan to a foreign national if adequate down payment is made (usually 35% or more).
Jack Gillis, M.B.A., J.D.
Jack Gillis Realty Advisors
Nathan Grace Real Estate, Broker
5619 Dyer Street | Suite 100
Dallas, TX 75206