  An action for a prospect of a $p$-adic open superstring on a target Minkowski
space is proposed. The action is constructed for `worldsheet' fields taking
values in the $p$-adic field $\mathbb{Q}_p$, but it is assumed to be obtained
from a discrete action on the Bruhat-Tits tree. This action is proven to have
an analog of worldsheet supersymmetry and the superspace action is also
constructed in terms of superfields. The action does not have conformal
symmetry, however it is implemented in the definition of the amplitudes. The
tree-level amplitudes for this theory are obtained for $N$ vertex operators
corresponding to tachyon superfields and a Koba-Nielsen formula is obtained.
Finally, four-point amplitudes are computed explicitly and they are compared to
previous work on $p$-adic superstring amplitudes.
