Honestly you might be able to, really does depend on the power supply though.
It should have shipped with a 500W PSU, which is enough to run an HD 6850.
However, it also needs a 6-pin PCIe connector (though some require 2), which the PSU may or may not have.
I would say it'd be smart to get a Corsair CX500 V2
500W, has 2 6+2-pin PCIe connectors, and is fairly inexpensive ($50 till 4/16, and a $20 rebate).
Please read through the thread thoroughly before responding.
Nobody wants to read a wall of text, formatting is your friend.
i5 3570k | 8GB G.Skill 1600MHz | R9 290 | SeaSonic 750X