Anisotropy and absorption are critical to the modeling and analysis of seismic amplitude, phase, and traveltime data. Neglecting any of these phenomena, which are often both operating simultaneously, degrades the resolution and interpretability of migrated images. However, a full accounting of anisotropy and anelasticity is computationally complex and expensive. One strategy for accommodating these aspects of wave propagation, while keeping the cost and complexity under control, is to do so within an acoustic approximation. We have set up a procedure for solving the time-domain viscoacoustic wave equation for tilted transversely isotropic (TTI) media, based on a standard linear solid model and, from this, develop a viscoacoustic reverse time migration (Q-RTM) algorithm. In this approach, amplitude compensation occurs within the migration process through a manipulation of attenuation and phase dispersion terms in the time-domain differential equations. Specifically, the back-propagation operator is constructed by reversing the sign only of the amplitude loss operators, but not the dispersion-related operators, a step made possible by reformulating the absorptive TTI equations such that the loss and dispersion operators appear separately. The scheme is tested on synthetic examples to examine the capacity of viscoacoustic RTM to correct for attenuation and the overall stability of the procedure.