By employing ab initio electronic-structure calculations combined with the nonequilibrium Green's function technique, we study the dependence of the thermopower Q on the conformation in biphenyl-based single-molecule junctions. For the series of experimentally available biphenyl molecules, alkyl side chains allow us to gradually adjust the torsion angle ϕ between the two phenyl rings from 0^∘ to 90^∘ and to control in this way the degree of π-electron conjugation. Studying different anchoring groups and binding positions, our theory predicts that the absolute values of the thermopower decrease slightly towards larger torsion angles, following an a+bcos²ϕ dependence. The anchoring group determines the sign of Q and a,b simultaneously. Sulfur and amine groups give rise to Q,a,b>0, while for cyano, Q,a,b<0. The different binding positions can lead to substantial variations of the thermopower mostly due to changes in the alignment of the frontier molecular orbital levels and the Fermi energy. We explain our ab initio results in terms of a π-orbital tight-binding model and a minimal two-level model, which describes the pair of hybridizing frontier orbital states on the two phenyl rings. The variations of the thermopower with ϕ seem to be within experimental resolution.