You can search the HUD website for apartments but thats about it. To my knowledge only agents can access that information. Your local housing authority should have a wall or list of homes that are available through their program. No home is owned by HUD, in fact individual homeowners do. Ask a local Realtor to do a search for the type of home you want to lease and they can do their due diligence by calling the listing Realtor to see if they accept public housing vouchers ( a.k.a Section 8). If you really want to take it into your own hands then search craigslist and call the owners yourself.
Tina, that might be difficult to do. I've personally never seen a public search that lets you look specifically for HUD approved rental homes. Your best bet might be to talk to an Agent that deals with those who can provide you a list, or help guide you. If I hear of any public search that allows you to do that, I'll let you know. Good luck!