  Given a graded complete intersection ideal $J = (f_1, \dots, f_c) \subseteq
k[x_0, \dots, x_n] = S$, where $k$ is a field of characteristic $p > 0$ such
that $[k:k^p] < \infty$, we show that if $S/J$ has an isolated non-F-pure point
then the Frobenius action on top local cohomology $H^{n+1-c}_\mathfrak{m}(S/J)$
is injective in sufficiently negative degrees, and we compute the least degree
of any kernel element. If $S/J$ has an isolated singularity, we are also able
to give an effective bound on $p$ ensuring the Frobenius action on
$H^{n+1-c}_\mathfrak{m}(S/J)$ is injective in all negative degrees, extending a
result of Bhatt and Singh in the hypersurface case.
