SPINspiral analyzes gravitational-wave signals from stellar-mass binary inspirals detected by ground-based interferometers such as LIGO and Virgo. It performs parameter estimation on these signals using Markov-chain Monte-Carlo (MCMC) techniques. This analysis includes the spins of the binary components. Written in C, the package is modular; its main routine is as small as possible and calls other routines, which perform tasks such as reading input, choosing and setting (starting or injection) parameters, and handling noise. Other routines compute overlaps and likelihoods, contain the MCMC core, and manage more general support functions and third-party routines.