I have seen several questions related to race and the history of black people in ancient Rome which makes it pretty clear that Romans did not care much about skin color but more about social origins. Therefore it could makes sense to have black senators. Do we have evidence of it?
Additional question: I guess we don't have a surviving list of all the senators of ancient Rome but how many can we name? What percentage does that represent?
I have never come across physical descriptions of senators. I recall authors like Suetonius or Tacitus would mention someone's physical description in a more in depth look at a particular person. Suetonius described the appearances of emperors in De Vita Caesarum.
Romans had slaves from all over the empire but there were also freedmen from all over the empire. It isn't impossible to have had a black senator but brown skin would already have been very common seeing as Rome is in Italy and many patricians came from all over the empire.