  The detections of gravitational waves produced in mergers of binary black
holes (BH) and neutron stars (NS) by LIGO/Virgo have stimulated interest in the
origin of the progenitor binaries. Dense stellar systems - globular and nuclear
star clusters - are natural sites of compact object binary formation and
evolution towards merger. Here we explore a new channel for the production of
binary mergers in clusters, in which the tidal field of the cluster secularly
drives the binary to high eccentricity (even in the absence of a central
massive black hole) until gravitational wave emission becomes important. We
employ the recently developed secular theory of cluster tide-driven binary
evolution to compute present day merger rates for BH-BH, NS-BH and NS-NS
binaries, varying cluster potential and central concentration of the binary
population (but ignoring cluster evolution and stellar flybys for now). Unlike
other mechanisms, this new dynamical channel can produce a significant number
of mergers out to cluster-centric distances of several pc. For NS-NS binaries
we find merger rates in the range $0.01-0.07$ Gpc$^{-3}$ yr$^{-1}$ from
globular clusters and $0.1-0.2$ Gpc$^{-3}$ yr$^{-1}$ from cusped nuclear
clusters. For NS-BH and BH-BH binaries we find small merger rates from globular
clusters, but a rate of $0.1 - 0.2$ Gpc$^{-3}$ yr$^{-1}$ from cusped nuclear
clusters, contributing to the observed LIGO/Virgo rate at the level of several
per cent. Therefore, cluster tide-driven mergers constitute a new channel that
can be further explored with current and future gravitational wave detectors.
