Rapper Future -- Racking Up Baby Mamas?

Future -- the rapper behind the hit "Same Damn Time" -- may have to multitask when it comes to parenting duties ... 'cause ANOTHER woman is claiming he knocked her up.

TMZ has learned the most recent potential baby mama filed a lawsuit against Future in Georgia earlier this month ... claiming she gave birth to his son on December 4th. She also wants Future to start paying child support for the newborn STAT.

The woman makes it clear in docs, if Future disputes the paternity ... she wants a judge order him to take a DNA test ... and make it official.

As we previously reported ... Future just settled another baby mama paternity suit back in January -- and agreed to pay $1,662 a month in child support for his 10-year-old son.