This study presents a Recursive Least Squares (RLS) based approach for adaptive control allocation. The algorithm is premised on the least squares based modification for adaptive control and guarantees convergence under the condition of linear independent data. We modified the adaptation law for control allocation to adapt the control effectiveness vector. The adaptive control allocation is presented with an (extended) Incremental Nonlinear Dynamic Inversion (INDI) controller. We compared two different RLS parameterizations with regularization for handling the nullspace of the input matrix of an overactuated system. The adaptive control allocation is successfully tested in simulation with a nonlinear hexacopter model and under realistic noise levels.