We formulate a self-consistent field theory for polyelectrolyte brushes in the presence of counterions. We numerically solve self-consistent field equations for weak coupling cases and study the monomer density profile, the distribution of counterions, and the total charge distribution. We also study scaling relations for brush height and compare them with the predictions based on other theories. We find a weak dependence of brush height on grafting density. We fit the counterion distribution outside a brush using the Gouy-Chapman solution for a charged virtual plane. We calculate the amount of counterions outside the brush and find that it saturates as the charge of polyelectrolytes increases in a weak coupling case.