The biggest problem would be how to restrain the astronaut aboard the craft during the launch. Unlike a man rated spacecraft, cargo carriers have no seats, and a seat on a spacecraft needs to be capable of holding an astronaut in place during liftoff while the ship is undergoing high and variable "g" forces, lots of vibration and acoustic pummelling and weird changes in attitude as the craft rotates and tips over during the launch phase. Then the seat needs to keep the astronaut in place in zero "g" as the ship coasts in orbit, and not let him be buffeted too severely as the ship makes small burns for orbital correction and moving to dock with the ISS itself.
Since spacecraft are very high performance craft with little margin for error and payloads calculated almost to the gram, the extra weight of the seat and support mechanism would need to be compensated for by removing some of the cargo, which kind of defeats the purpose.
The other thing which makes ships "man rated" are things like life support (you will need to somehow keep the astronaut alive for 3-5 days on board the spacecraft, meaning more cargo is displaced for oxygen tanks, water and some sort of way for the guy to eat). There is also a lot of thought given to being able to separate the capsule from the rocket should some sort of disaster occur during launch, but cargo capsules typically don't have this mechanism attached (the Dragon capsule is the only exception to date, having built in rockets around the "skirt" rather than a "tractor rocket" on a detachable tower). Since we can assume the astronaut is planning to return via the Soyuz capsule attached to the ISS, we can overlook the lack of reentry protection if you are not using a Dragon capsule.
So this is one of those plans which is barely feasible even in theory, and by the time you added on all the stuff needed to get the guy in orbit, you may as well have just flown in a man rated capsule and mated it to the rocket in the first place.