The pursuit of novel sustainable materials is driving advancements in polymer science, with the consolidation of furfural and hydroxymethylfurfural derivatives as key renewable building blocks. 3,4-Di(furan-2-yl)cyclobutane-1,2-dicarboxylic acid (CBDA) is a highly promising rigid-structure biobased monomer that is readily synthesized from furfural. In this study, we expanded the scope of CBDA-based polymers by synthesizing this platform molecule and investigating its polymerization with a series of aliphatic diols of varying chain lengths. CBDA was successfully synthesized from furfural-derived 3-(2-furyl)acrylic acid through a green and efficient UV-mediated solid-state dimerization reaction. Subsequent polymerization was carried out in bulk via a two-step method. The success of the polymerization was confirmed through ATR-FTIR, 1H NMR, and 13C CP/MAS NMR spectroscopy. The resulting polymers presented average molecular weights () of up to 11 200 g mol−1. Thermogravimetric analysis (TGA) revealed good thermal stability, with a Td10% ranging from 263 to 284 °C and 50% weight retention observed up to 388 °C. Furthermore, DSC analysis indicated that the glass transition temperature of the polymers could be tailored, varying from 6 to 52 °C depending on the chain length of the utilized diol. These results underscore the potential of CBDA as a renewable rigid monomer for the development of sustainable biobased materials.