This paper numerically studies the bifurcation buckling load of steel angle members affected by random corrosion pits. Six million Monte Carlo simulations are conducted, in which the effects of member length, section type, area loss ratio, and corrosion depth on the bifurcation buckling load of steel angles are considered. The key statistical characteristics of the reduction factors of buckling load for steel angles are analyzed. A probability-based relationship between the reduction factor of buckling load and the area loss ratio of steel angles is also proposed for the practical design. It is found that corrosion can potentially change the buckling mode of steel angle members from flexural buckling to torsional buckling. When the member length is small, the bifurcation buckling load of the steel angle is significantly affected by the corrosion depth. However, with the increase in member length, the effect of corrosion depth tends to decrease. The reduction factors of the buckling load of steel angles follow a normal distribution. A larger area loss ratio will result in a larger standard deviation of the reduction factors. For steel angles with the same area loss ratio, the mean values of the reduction factors of different section types are very close.