Using a data set of 2.93 fb$^{-1}$ taken at a center-of-mass energy of $\sqrt{s}$ = 3.773 GeV with the BESIII detector at the BEPCII collider, we measure the process $e^+e^-→ J/ψγ→ μ^+μ^-γ$ and determine the product of the branching fraction and the electronic width $\mathcal B_{μμ}⋅ Γ_{ee} = (333.4 ± 2.5_{\rm stat} ± 4.4_{\rm sys})$~eV. Using the earlier-published BESIII result for $\mathcal B_{μμ}$ = (5.973 $±$ 0.007$_{\rm stat}$ $±$ 0.037$_{\rm sys}$)\%, we derive the $J/ψ$ electronic width $Γ_{ee}$~= (5.58 $±$ 0.05$_{\rm stat}$ $±$ 0.08$_{\rm sys}$) keV.