Using a kinetic model for the ions and adiabatic electrons, we solve a steady state, electron-repelling magnetic presheath in which a uniform magnetic field makes a small angle α << 1 (in radians) with the wall. The presheath characteristic thickness is the typical ion gyroradius pi. The Debye length λD and the collisional mean free path of an ion λmfp satisfy the ordering λD << pi << αλmfp, so a quasineutral and collisionless model is used. We assume that the electrostatic potential is a function only of distance from the wall, and it varies over the scale pi. Using the expansion in α << 1, we derive an analytical expression for the ion density that only depends on the ion distribution function at the entrance of the magnetic presheath and the electrostatic potential profile. Importantly, we have added the crucial contribution of the orbits in the region near the wall. By imposing the quasineutrality equation, we derive a condition that the ion distribution function must satisfy at the magnetic presheath entrance - the kinetic equivalent of the Chodura condition. Using a boundary condition that satisfies the kinetic Chodura condition, we find a numerical solution for the self-consistent electrostatic potential, ion density and flow across the magnetic presheath for several values of α. Our numerical results also include the distribution of ion velocities at the Debye sheath entrance. We find that at small values of α there are substantially fewer ions travelling with a large normal component of the velocity into the wall.