We propose an orthogonal chirp waveform design for underwater acoustic (UW-A) communications and analyze the cross-correlation characteristics of orthogonal chirp waveforms in coherent and non-coherent detections. We consider information symbols are carried over proposed M-ary orthogonal chirp waveforms for UW-A transmissions. Moreover, we develop a coherent and an optimal non-coherent receivers based on proposed chirp waveforms. Explicit derivations include closed-form expressions for cross-correlation coefficients, and theoretical bit-error-rate (BER) of coherent and non-coherent receivers. Performance of M-ary orthogonal chirp waveforms is evaluated in water tank experiments. Therefore, we have demonstrated the effectiveness of proposed M-ary orthogonal chirp modulation in UW-A multipath fading channel.