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This brief proposes a design method for a digital fractional order Savitzky-Golay differentiator (DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order for estimating the fractional order derivative of the contaminated signal. The proposed method calculates the moving window's weights using the polynomial least-squares method and the Riemann-Liouville fractional order derivative definition, and then computes the fractional order derivative of the given signal using the convolution between the weights and the signal, instead of the complex mathematical deduction. Hence, the computation time is greatly improved. Frequency-domain analysis reveals that the proposed differentiator is essentially a fractional order low-pass filter. Experiments demonstrate that the proposed DFOSGD can accurately estimate the fractional order derivatives of both noise-free signal and contaminated signal.