Magnetometers are essential sensors for attitude estimation in small spacecraft due to their robust, inexpensive, and lightweight characteristics. However, the raw measurements contain sensor errors. These errors degrade the attitude estimation accuracy. This study proposes a complete real-time attitude-independent magnetometer calibration algorithm for spinning spacecraft. The recursive algorithm aims to estimate the full error state, bias, scale factor, and non-orthogonality corrections in real-time and without any attitude information. The well-known attitude-independent observation based on the magnitude of the sensed magnetic field is aided by newly introduced quasi-measurements to build the algorithm. The algorithm is tested with both simulations and actual spacecraft data. Four quasi-measurements, which are derived using dynamic characteristics of the spacecraft, considerably improve the convergence characteristics of the filter and the estimation accuracy.