Abstract Exclusive $${{{\uprho _{}^{}} _{}^{}}{{\left( {770}\right) }{}_{}^{}}} ^{0}$$ ρ7700 photoproduction is measured for the first time in ultraperipheral pPb collisions at $$\sqrt{\smash b{s_{_{\mathrm {NN}}} = 5.02\,\text {Te}\text {V} $$ sNN=5.02Te with the CMS detector. The cross section $$\sigma ({\upgamma _{}^{}} \mathrm{p}\rightarrow {{{\uprho _{}^{}} _{}^{}}{{\left( {770}\right) }{}_{}^{}}} ^{0}\mathrm{p})$$ σ(γp→ρ7700p) is $$11.0 \pm 1.4\,\text {(stat)} \pm 1.0\,\text {(syst)} $$ 11.0±1.4(stat)±1.0(syst) $$\mu $$ μ b at $$\langle W_{{\upgamma _{}^{}} \mathrm{p}}\rangle = 92.6\,\text {Ge}\text {V} $$ ⟨Wγp⟩=92.6Ge for photon–proton centre-of-mass energies $$W_{{\upgamma _{}^{}} \mathrm{p}}$$ Wγp between 29 and $$213\,\text {Ge}\text {V} $$ 213Ge . The differential cross section $$\mathrm {d}\sigma /\mathrm {d}|t |$$ dσ/d|t| is measured in the interval $$0.025< |t | < 1\,\text {Ge}\text {V} ^{2}$$ 0.025<|t|<1Ge2 as a function of $$W_{{\upgamma _{}^{}} \mathrm{p}}$$ Wγp , where t is the squared four-momentum transfer at the proton vertex. The results are compared with previous measurements and theoretical predictions. The measured cross section $$\sigma ({\upgamma _{}^{}} \mathrm{p}\rightarrow {{{\uprho _{}^{}} _{}^{}}{{\left( {770}\right) }{}_{}^{}}} ^{0}\mathrm{p})$$ σ(γp→ρ7700p) has a power-law dependence on the photon–proton centre-of-mass, consistent with electron–proton collision measurements performed at HERA. The $$W_{{\upgamma _{}^{}} \mathrm{p}}$$ Wγp dependence of the exponential slope of the differential cross section $$\mathrm {d}\sigma /\mathrm {d}|t |$$ dσ/d|t| is also measured.