Proton resonant states in $^{23}\mathrm{Al}$ have been investigated for the first time by the resonant elastic and inelastic scattering of $^{22}\mathrm{Mg}$$+p$ with a $^{22}\mathrm{Mg}$ beam at 4.38 MeV/nucleon bombarding a thick (CH${}_{2}$)${}_{n}$ target. The low-energy $^{22}\mathrm{Mg}$ beam was separated by the CNS radioactive ion beam separator (CRIB). The energy spectra of recoiled protons were measured at average scattering angles of ${\ensuremath{\theta}}_{\mathrm{lab}}\ensuremath{\approx}4{}^{\ifmmode^\circ\else\textdegree\fi{}},17{}^{\ifmmode^\circ\else\textdegree\fi{}}$ and $23{}^{\ifmmode^\circ\else\textdegree\fi{}}$. A new state has been observed at ${E}_{x}=3.00$ MeV with a spin-parity assignment of ($3/{2}^{+}$). In addition, resonant inelastic scattering has populated three more states at excitation energies of 3.14, 3.26, and 3.95 MeV, with proton decay to the first excited state in $^{22}\mathrm{Mg}$ being observed. The new state at 3.95 MeV has been assigned a spin-parity of ${J}^{\ensuremath{\pi}}=(7/{2}^{+})$. The resonant parameters were determined by an $R$-matrix analysis of the excitation functions with a SAMMY-M6-BETA code. The core-excited structure of $^{23}\mathrm{Al}$ is discussed within a shell-model picture. The stellar reaction rate of the $^{22}\mathrm{Mg}$($p,\ensuremath{\gamma}$)$^{23}\mathrm{Al}$ reaction has been reevaluated, and the revised total reaction rate is about 40% greater than the previous result for temperatures beyond ${T}_{9}=0.3$.