Conjugated polymers with nearly planar backbones have been the most commonly investigated materials for organic-based electronic devices. More twisted polymer backbones have been shown to achieve larger open-circuit voltages in solar cells, though with decreased short-circuit current densities. We systematically impose twists within a family of poly(hexylthiophene)s and examine their influence on the performance of polymer:fullerene bulk heterojunction (BHJ) solar cells. A simple chemical modification concerning the number and placement of alkyl side chains along the conjugated backbone is used to control the degree of backbone twisting. Density functional theory calculations were carried out on a series of oligothiophene structures to provide insights on how the sterically induced twisting influences the geometric, electronic, and optical properties. Grazing incidence X-ray scattering measurements were performed to investigate how the thin-film packing structure was affected. The open-circuit voltage and charge-transfer state energy of the polymer:fullerene BHJ solar cells increased substantially with the degree of twist induced within the conjugated backbone-due to an increase in the polymer ionization potential-while the short-circuit current decreased as a result of a larger optical gap and lower hole mobility. A controlled, moderate degree of twist along the poly(3,4-dihexyl-2,2':5',2 ''-terthiophene) (PDHTT) conjugated backbone led to a 19% enhancement in the open-circuit voltage (0.735 V) vs poly(3-hexylthiophene)-based devices, while similar short-circuit current densities, fill factors, and hole-carrier mobilities were maintained. These factors resulted in a power conversion efficiency of 4.2% for a PDHTT:[6,6]-phenyl-C-71-butyric acid methyl ester (PC71BM) blend solar cell without thermal annealing. This simple approach reveals a molecular design avenue to increase open-circuit voltage while retaining the short-circuit current.