We present Exo-Transmit, a software package to calculate exoplanet transmission spectra for planets of varied composition. The code is designed to generate spectra of planets with a wide range of atmospheric composition, temperature, surface gravity, and size, and is therefore applicable to exoplanets ranging in mass and size from hot Jupiters down to rocky super-Earths. Spectra can be generated with or without clouds or hazes with options to (1) include an optically thick cloud deck at a user-specified atmospheric pressure or (2) to augment the nominal Rayleigh scattering by a user-specified factor. The Exo-Transmit code is written in C and is extremely easy to use. Typically the user will only need to edit parameters in a single user input file in order to run the code for a planet of their choosing. Exo-Transmit is available publicly on Github with open-source licensing at https://github.com/elizakempton/Exo_Transmit.