  We study worldsheet instantons in holographic type IIA backgrounds directly
in string theory. The first background is a dimensional reduction of
AdS$_7\times S^4$ and is dual to the maximally supersymmetric Yang-Mills theory
on $S^5$. The second background is AdS$_4\times \mathbf{C}P^3$ dual to ABJM in
the type IIA limit. We compute the one-loop partition function of the
fundamental string in these backgrounds and show that the result is in exact
agreement with field theory predictions. We argue that for higher rank
instantons, the string partition function takes a product form of the single
instanton partition function times the contribution of two orbifolds on the
worldsheet. We determine the orbifold factor to be $n^{-3/2}$ where $n$ is the
instanton rank. With this result, we reproduce the series of non-perturbative
corrections in $\alpha'$ to the planar $S^5$ free energy. When studying the
worldsheet instanton partition function on $\mathbf{C}P^3$, we encounter twelve
fermionic and twelve bosonic zero modes. By deforming the ABJM theory, the
zero-modes are lifted and consequently the tower of worldsheet instantons can
be evaluated and matched to known results in the QFT. As a by-product, we
determine a series of higher rank instanton corrections to the free energy of
the mass-deformed and orbifolded ABJ(M) theory.
