As far as I know, you can. You do not need to be US citizen to buy real estate in the US. If you have money or can secure financing, there is no problems. To secure a mortgage, a bank will look for your tax filings, full time job status, income etc. If all these documents are available, I do not see why you cannot buy a house in the US. When I bought mine, I only had work visa. I do not recall anyone verifying my status with INS.