Application of the radial velocity (RV) technique in the near-infrared is valuable because of the diminished impact of stellar activity at longer wavelengths, making it particularly advantageous for the study of late-type stars but also for solar-type objects. In this paper, we present the IGRINS RV open-source python pipeline for computing infrared RV measurements from reduced spectra taken with IGRINS, an R~{lambda}/{Delta}{lambda}~45000 spectrograph with simultaneous coverage of the H-band (1.49-1.80{mu}m) and K-band (1.96-2.46{mu}m). Using a modified forward-modeling technique, we construct high-resolution telluric templates from A0 standard observations on a nightly basis to provide a source of common-path wavelength calibration while mitigating the need to mask or correct for telluric absorption. Telluric standard observations are also used to model the variations in instrumental resolution across the detector, including a yearlong period when the K-band was defocused. Without any additional instrument hardware, such as a gas cell or laser frequency comb, we are able to achieve precisions of 26.8m/s in the K-band and 31.1m/s in the H-band for narrow-line hosts. These precisions are empirically determined by a monitoring campaign of two RV standard stars, as well as the successful retrieval of planet-induced RV signals for both HD189733 and {tau}BooA; furthermore, our results affirm the presence of the Rossiter-McLaughlin effect for HD189733. The IGRINS RV pipeline extends another important science capability to IGRINS, with publicly available software designed for widespread use.

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