I present the IGRINS RV open source python pipeline for computing infrared RV measurements from reduced spectra taken with IGRINS, a R~45,000 spectrograph with simultaneous coverage of the H band and K band. Using a modified forward modeling technique, the pipeline constructs 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. Without any additional equipment, such as a gas cell or laser frequency comb, the wide wavelength range of IGRINS allows the pipeline to achieve precisions of 25.8 m/s in the K band and 33.9 m/s in the H band for narrow-line hosts. These precisions are validated by a monitoring campaign of two RV standard stars as well as the successful retrieval of planet-induced RV signals for both HD 189733 and Tau Boo A.