  In this paper, we discuss spherically symmetric wormhole solutions in
$f(R,T)$ modified theory of gravity by introducing well-known non-commutative
geometry in terms of Gaussian and Lorentizian distributions of string theory.
For some analytic discussion, we consider an interesting model of $f(R,T)$
gravity defined by $f(R,T)=f_{1}(R)+\lambda T$. By taking two different choices
for the function $f_{1}(R)$, that is, $f_{1}(R)=R$ and $f_{1}(R)=R+\alpha
R^{2}+\gamma R^{n}$, we discuss the possible existence of wormhole solutions.
In the presence of non-commutative Gaussian and Lorentizian distributions, we
get exact and numerical solutions for both these models. By taking appropriate
values of the free parameters, we discuss different properties of these
wormhole models analytically and graphically. Further, using equilibrium
condition, it is found that these solutions are stable. Also, we discuss the
phenomenon of gravitational lensing for the exact wormhole model and it is
found that the deflection angle diverges at wormhole throat.
