Secure Device Pairing (SDP) relies on an out-of-band channel to authenticate devices. This requires a common hardware interface, which limits the use of existing SDP systems. We propose to use short-range acoustic communication for the initial pairing. Audio hardware is commonly available on existing off-the-shelf devices and can be accessed from user space without requiring firmware or hardware modifications. We improve upon previous approaches by designing Acoustic Integrity Codes (AICs): a modulation scheme that provides message authentication on the acoustic physical layer. We analyze their security and demonstrate that we can defend against signal cancellation attacks by designing signals with low autocorrelation. Our system can detect overshadowing attacks using a ternary decision function with a threshold. In our evaluation of this SDP scheme's security and robustness, we achieve a bit error ratio below 0.1% for a net bit rate of 100 bps with a signal-to-noise ratio (SNR) of 14 dB. Using our open-source proof-of-concept implementation on Android smartphones, we demonstrate pairing between different smartphone models.