Scrambling of quantum information can conveniently be quantified by so-called out-of-time-order correlators (OTOCs), i.e., correlators of the type 〈[W_{τ},V]^{†}[W_{τ},V]〉, whose measurements present a formidable experimental challenge. Here we report on a method for the measurement of OTOCs based on the so-called two-point measurement scheme developed in the field of nonequilibrium quantum thermodynamics. The scheme is of broader applicability than methods employed in current experiments and provides a clear-cut interpretation of quantum information scrambling in terms of nonequilibrium fluctuations of thermodynamic quantities, such as work and heat. Furthermore, we provide a numerical example on a spin chain which highlights the utility of our thermodynamic approach when understanding the differences between integrable and ergodic behaviors. We also discuss how the method can be used to extend the reach of current experiments.