  New phases of matter emerge at the edge of magnetic instabilities. In local
moment systems, such as heavy fermions, the magnetism can be destabilized by
pressure, chemical doping, and, rarely, by magnetic field, towards a
zero-temperature transition at a quantum critical point (QCP). Even more rare
are instances of QCPs induced by pressure or doping in itinerant moment
systems, with no known examples of analogous field-induced \textit{T} = 0
transitions. Here we report the discovery of a new itinerant antiferromagnet
with no magnetic constituents, in single crystals of Ti$_3$Cu$_4$ with $T_N$ =
11.3 K. Band structure calculations point to an orbital-selective, spin density
wave ground state, a consequence of the square net structural motif in
Ti$_3$Cu$_4$. A small magnetic field, $H_C$ = 4.87 T, suppresses the long-range
order via a continuous second-order transition, resulting in a field-induced
QCP. The magnetic Gr\"uneisen ratio diverges as $H \rightarrow H_C$ and
$T\rightarrow0$, with a sign change at $H_C$ and $T^{-1}$ scaling at $H~=~H_C$,
providing evidence from thermodynamic measurements for quantum criticality for
$H \parallel c$. Non-Fermi liquid (NFL) to Fermi liquid (FL) crossover is
observed close to the QCP, as revealed by the power law behavior of the
electrical resistivity.
