In this article we study a robust estimator for the spectrum of stationary processes under presence of additive outliers. The estimator is called M periodogram and it is based on the square sums of robust estimators of the Fourier's coefficients for the spectral representation of stationary processes. The estimates of the coefficients are obtained using the M-estimators with different lost functions. Theoretical results show that the asymptotic properties of the classic and robust periodograms are equivalent. Empirical studies using Monte Carlo simulation show the performance of the estimator in the spectral density estimation of ARFIMA(p,d,q) processes.