The azimuthal correlation angle, $$\Delta \phi $$ , between the scattered lepton and the leading jet in deep inelastic $$e^{\pm }p$$ scattering at HERA has been studied using data collected with the ZEUS detector at a centre-of-mass energy of $$\sqrt{s} = 318 {\,\text {Ge}\hspace{-0.66666pt}\text {V}}$$ , corresponding to an integrated luminosity of $$326 \,\text {pb}^{-1}$$ . A measurement of jet cross sections in the laboratory frame was made in a fiducial region corresponding to photon virtuality $$10 {\,\text {Ge}\hspace{-0.66666pt}\text {V}}^2< Q^2 < 350 {\,\text {Ge}\hspace{-0.66666pt}\text {V}}^2$$ , inelasticity $$0.04< y < 0.7$$ , outgoing lepton energy $$E_e > 10 {\,\text {Ge}\hspace{-0.66666pt}\text {V}}$$ , lepton polar angle $$140^\circ< \theta _e < 180^\circ $$ , jet transverse momentum $$2.5 {\,\text {Ge}\hspace{-0.66666pt}\text {V}}< p_\textrm{T,jet} < 30 {\,\text {Ge}\hspace{-0.66666pt}\text {V}}$$ , and jet pseudorapidity $$-1.5< \eta _\textrm{jet} < 1.8$$ . Jets were reconstructed using the $$k_\textrm{T}$$ algorithm with the radius parameter $$R = 1$$ . The leading jet in an event is defined as the jet that carries the highest $$p_\textrm{T,jet}$$ . Differential cross sections, $$d\sigma /d\Delta \phi $$ , were measured as a function of the azimuthal correlation angle in various ranges of leading-jet transverse momentum, photon virtuality and jet multiplicity. Perturbative calculations at $$\mathcal {O}(\alpha _{s}^2)$$ accuracy successfully describe the data within the fiducial region, although a lower level of agreement is observed near $$\Delta \phi \rightarrow \pi $$ for events with high jet multiplicity, due to limitations of the perturbative approach in describing soft phenomena in QCD. The data are equally well described by Monte Carlo predictions that supplement leading-order matrix elements with parton showering.