  The antiferromagnet and semimetal EuCd$_2$As$_2$ has recently attracted a lot
of attention due to a wealth of topological phases arising from the interplay
of topology and magnetism. In particular, the presence of a single pair of Weyl
points is predicted for a ferromagnetic configuration of Eu spins along the
$c$-axis in EuCd$_2$As$_2$. In the search for such phases, we investigate here
the effects of hydrostatic pressure in EuCd$_2$As$_2$. For that, we present
specific heat, transport and $\mu$SR measurements under hydrostatic pressure up
to $\sim\,2.5\,$GPa, combined with {\it ab initio} density functional theory
(DFT) calculations. Experimentally, we establish that the ground state of
EuCd$_2$As$_2$ changes from in-plane antiferromagnetic (AFM$_{ab}$) to
ferromagnetic at a critical pressure of $\,\approx\,$2\,GPa, which is likely
characterized by the moments dominantly lying within the $ab$ plane
(FM$_{ab}$). The AFM$_{ab}$-FM$_{ab}$ transition at such a relatively low
pressure is supported by our DFT calculations. Furthermore, our experimental
and theoretical results indicate that EuCd$_2$As$_2$ moves closer to the
sought-for FM$_c$ state (moments $\parallel$ $c$) with increasing pressure
further. We predict that a pressure of $\approx$\,23\,GPa will stabilize the
FM$_c$ state, if Eu remains in a 2+ valence state. Thus, our work establishes
hydrostatic pressure as a key tuning parameter that (i) allows for a continuous
tuning between magnetic ground states in a single sample of EuCd$_2$As$_2$ and
(ii) enables the exploration of the interplay between magnetism and topology
and thereby motivates a series of future experiments on this magnetic Weyl
semimetal.
