  In the context of $\rm AdS_3/CFT_2$, we investigate holographic correlators
of the stress tensor of a conformal field theory (CFT) on a torus in this work.
To calculate the correlators of the stress tensor, we employ the
Einstein-Hilbert theory of gravity and perturbatively solve Einstein's equation
in the bulk. We offer an explicit prescription to develop a recurrence relation
that makes it simple to compute higher point correlators. The correlators and
the recurrence relation are found to be consistent with what is known in CFTs.
Following the spirit of the proposed cutoff $\rm AdS$/$T\bar{T}$ CFT
holography, we then expand our computation program to investigate holographic
torus correlators at a finite cutoff in the $\rm AdS_3$. A parallel recurrence
relation associated with higher point correlators can be obtained.
