First, as a former Army soldier, thank you for your service!! The short answer is yes you can.
The longer answer is that if you were honorably discharged and have a credit score that qualifies (good rule of thumb is 620 or greater though there are exceptions) you would probably be qualified for a VA loan. A VA loan is a $0.00 down payment loan. If you link up with a local real estate agent that is a veteran or has VA experience, they can guide you to a VA lender and guide you through the rest of the process.
The ideal scenario is to put no money down and find a home where you negotiate for closing cost assistance from the seller so that you basically buy the home for no money at closing. It is a benefit we have for putting our life on the line for our country. Good luck and God Speed!!