Check the Mass Effect Timeline for some history.

Since there's nothing specific in there about Wrex's date of birth, let's try some extrapolation before /u/Cloud1515 has an aneurysm.

• Mass Effect - Around Eden Prime War: Conflict starts in 2183 and Shepard meets Wrex that year. Wrex has been off Tuchanka for 300 years at this point...IIRC, that's what we find out in-game from him.
• Leaving Tuchanka: So Wrex left in 1883 CE; the Geth-Quarian (Morning War) took place in 1895 CE as a point of reference...he's already off planet by then.
• Krogan Rebellions: 100 years as stated; from 700 CE to 800 CE. Wrex obviously was born after 800 CE since his father Jarrod was making a call to arms after the Rebellions and him and Wrex had their Crush and fight at some point after that.
• Info on Wrex's Early Life: Wrex was a young tribe leader in Clan Urdnot. It would stand to make sense that Wrex was only a few hundred years old at that point. Obviously, Wrex and his father Jarrod weren't going to meet at a Crush as leaders if Wrex wasn't one already.

So by the above info, here's what we can conclude:

• Wrex and his father, Jarrod, had their falling out around 1883 CE.
• Jarrod has likely been making the call to arms for a soon after the Krogan Rebellions ended or started making the call to arms several centuries after the Krogan Rebellions ended. I'm thinking it's closer to the second one.
• There's a gap of 1083 years from 800 CE (end of Krogan Rebellions) to 1883 CE (Wrex leaving Tuchanka), during which time Wrex was born.

So assuming Wrex was 300 hundred years old when he became a tribe leader, 400 years old when his father and him fought at the Crush, and then left Tuchanka soon after in 1883 CE, it could stand to reason Wrex was born around 1483 CE. We could deviate around 100-200 years give or take, and it would still make sense.

Logic, math, and some calculated assumptions, FTW.