This paper proposes a new DOA (direction of arrival) estimation method for an arbitrary triangular microphone arrangement. Using the phase rotation factors for the crosscorrelations between the adjacent-microphone signals, a general form of the integrated cross spectrum is derived. DOA estimation is reduced to a non-linear optimization problem of the general integrated cross spectrum. It is shown that a conventional DOA estimation for the equilateral triangular microphone arrangement is a special case of the proposed method. Sensitivity to the relative time-delay is derived in a closed form and demonstrated for different microphone arrangements. Simulation results demonstrate that the deviation of estimation error in the case of 20 dB SNR is less than 1 degree which is comparable to high resolution DOA estimation methods.