The $(p,t)$ reaction on ${}^{122}\mathrm{Sn}$ has been studied in a high resolution experiment at an incident proton energy of 26 MeV. The cross section angular distributions for transitions to 38 levels of ${}^{120}\mathrm{Sn}$ with an excitation energy up to $\ensuremath{\sim}3500\mathrm{keV}$ have been measured. Distorted wave Born approximation analysis of experimental angular distributions using double-folded potential for the exit channel has been done. This has made it possible to confirm previous spin and parity values and to propose new assignments for a large number of states. A shell-model study of ${}^{120}\mathrm{Sn}$ has been performed using a realistic effective interaction derived from the Paris nucleon-nucleon potential. The calculations have been carried out within the framework of the seniority scheme including states with seniority up to 4. Comparison of the calculated and experimental spectra shows a one-to-one correspondence between levels up to about 2.7 MeV excitation energy and lends support to some of the spin-parity assignments given in this work.