We report on the first measurement of exclusive single-photon muoproduction on the proton by COMPASS using 160 GeV/$c$ polarized $mu^+$ and $mu^-$ beams of the CERN SPS impinging on a liquid hydrogen target. We determine the dependence of the average of the measured $mu^+$ and $mu^-$ cross sections for deeply virtual Compton scattering on the squared four-momentum transfer $t$ from the initial to the final final proton. The slope $B$ of the $t$-dependence is fitted with a single exponential function, which yields $B=(4.3 pm 0.6_{text{stat}}_{- 0.3}^{+ 0.1}bigrvert_{text{sys}}) (text{GeV}/c)^{-2}$. This result can be converted into an average transverse extension of partons in the proton, $sqrt{langle r_{perp}^2 rangle} = (0.58 pm 0.04_{text{stat}}_{- 0.02}^{+ 0.01}bigrvert_{text{sys}})text{fm}$. For this measurement, the average virtuality of the photon mediating the interaction is $langle Q^2 rangle = 1.8,(text{GeV/}c)^2$ and the average value of the Bjorken variable is $langle x_{text{Bj}} rangle = 0.056$.
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