Spin-stabilization offers a simple attitude control solution, specifically for micro and nanosatellites, and has a large potential for implementation on numerous missions. This paper proposes an attitude estimation algorithm for spin satellites. The algorithm is loosely based on a filter proposed by Bar-Itzhack and Harman. Using a simple Kalman filter (KF) algorithm and only the magnetometer measurements, the spin axis and rate of the satellite are estimated. To improve the spin axis estimation accuracy the magnetometer measurements are corrected with a bias estimation algorithm. Two algorithms, the attitude filter and the magnetometer bias estimator, are integrated with a straightforward approach by merging them as a single KF algorithm. As a result, a pseudo-linear KF algorithm that estimates the spin parameters together with magnetometer bias terms is proposed. The algorithm is tested for a hypothetical nanosatellite via numerical simulations. The results are discussed in detail and suggestions for implementation of the algorithm are given.