  In this work, we study the dynamics of rogue waves in the partially
$\cal{PT}$-symmetric nonlocal Davey-Stewartson(DS) systems. Using the Darboux
transformation method, general rogue waves in the partially
$\cal{PT}$-symmetric nonlocal DS equations are derived. For the partially
$\cal{PT}$-symmetric nonlocal DS-I equation, the solutions are obtained and
expressed in term of determinants. For the partially $\cal{PT}$-symmetric DS-II
equation, the solutions are represented as quasi-Gram determinants. It is shown
that the fundamental rogue waves in these two systems are rational solutions
which arises from a constant background at $t\rightarrow -\infty$, and develops
finite-time singularity on an entire hyperbola in the spatial plane at the
critical time. It is also shown that the interaction of several fundamental
rogue waves is described by the multi rogue waves. And the interaction of
fundamental rogue waves with dark and anti-dark rational travelling waves
generates the novel hybrid-pattern waves. However, no high-order rogue waves
are found in this partially $\cal{PT}$-symmetric nonlocal DS systems. Instead,
it can produce some high-order travelling waves from the high-order rational
solutions.
