No such action is possible. Otherwise one would have a free action on a sphere of lower dimension linking the fixed point set. But such an action would give a free action of $G=\mathbf{Z}_p\times \mathbf{Z}_p$ on a sphere, violating the known fact that such a finite group cannot act freely on a finite complex with the homology of a sphere. Such an action of $G$ can be shown by a splicing argument to provide a periodic resolution of $\mathbf{Z}$ as a trivial $\mathbf{Z}[G]$-module, violating the fact that this group does not have periodic cohomology (by the Kunneth formula).

There is a bit of a disconnect between the title and the actual question. Usually a semifree action is one in which the only isotropy groups are the trivial group and the whole group. The actions with only finite isotropy groups, in the body of your question, are often called ``pseudofree'' actions. If a torus were to act pseudofreely on a sphere then a subgroup of the form $G=\mathbf{Z}_{p}\times \mathbf{Z}_{p}$ for some prime $p$ would act freely on the sphere. It is well-known that the latter group cannot act freely on a sphere because such an action would imply that the group has periodic cohomology, which $G$ does not. See Bredon's book Introduction to Compact Transformation Groups, for example.