In this work we develop a non-parametric method to estimate the input-passivity index of an unknown linear and time-invariant (LTI) system from iterative experiments based on the power method from numerical linear algebra. Inspired by the power method for estimating the H-infinity-norm (or l(2)-gain) from data, we propose an algorithm that time-reverses input-output data in order to emulate measurements of a virtual system whose l(2)-gain matches the passivity index of the original system under study. While the proposed method requires exciting the original system twice, we also introduce an improved sampling scheme where only one experiment per iteration is needed.