There's this girl claiming she's pregnant and my husbands the father of the child. I want to know if he can get a court ordered DNA test because I don't think the girl will do it freely?

If he wants to go for visits or if she tries to get child support, he can request ( make a motion) with the court for a test

Of course as Fr. Chuck said if he wants visitation or if she is wanting support then he makes a motion in court to have one ordered. Until then he shouldn't sign any papers i.e.. The because that legally claims the child as his own. This can't be done until the child is born though.

If she asks for child support, he can petition the court for a test. If he wants visitation, he can petition the court for a test. If he's just curious, no he can't force a test.