Black women technically received the right to vote at the same time as white women in the US (I assume this statement is about the USA) and after they were enfranchised in 1920, large numbers of black women did register to vote (in Florida, more black than white women registered). You had black women actively involved in the democratic process like Anna Simms Banks, who - after the 19th amendment was passed - was a fully credited delegate at the 7th Congressional District Republican Convention in Kentucky.
Of course, having the right to vote in law doesn’t mean that an oppressive society will allow you to exercise that right, and - particularly in Southern states - as black women (like black men) increasingly sought to participate in democratic processes, other means of voter suppression were put in place (new tests - like reading and interpreting the constitution, long lines for black voter registration etc).
ETA: I wrote 16th Amendment instead of 19th because I’m an idiot. Although no one has picked up on it yet, it’s too late for a sneaky edit ;)