Expanding on kingledion's answer, the interaction between positrons and electrons produces gamma radiation at a very specific energy as well: 512 kEV. Gamma radiation at that sort of energy will penetrate materials fairly easily, and most reaction materials like hydrogen or water will be virtually transparent to the inferno of gamma radiation, meaning most of the energy will simply pass through the reactor and end up irradiating the structural members of the vessel. The stuff you want to heat up isn't going to become as hot as you want (a superheated plasma for maximum ISP), while many of the things you would prefer to remain cool are at blazing temperatures.
You will actually have more success using anti protons, either interacting with normal matter protons in a beamed core engine, or beamed into the reaction mass flow to heat a larger quantity of water or hydrogen.
Antiprotons are made up of antiquarks, and the reaction of antiprotons creates a stew of charged particles. Most of these particles can be directed with magnetic or electrostatic fields so the energy they have is directed away from your ship, and hopefully out with the blazing plasma of your exhaust stream. Far less energy is going to be deposited on your ship's structural members, and the overall efficiency is going to be much greater (i.e you 100kg of antiprotons will provide far more usable energy and thrust than the same 100kg of positrons).
The difference between positron and anti protons
Simplified diagram of an antiproton rocket
So while an positron rocket seems to be going about things the hard way, using antiprotons to energize the rocket, either in a beam core engine or as a means of heating reactant seems to be the better way to go.