Kidney transplant outcomes are influenced by donor and recipient age, sex, HLA mismatch, donor type, anti-rejection medication adherence and disease recurrence, but variability in transplant outcomes remains unexplained. We hypothesise that donor and recipient polygenic burden for traits related to kidney function may also influence graft function. We assembled a cohort of 6,060 living and deceased kidney donor-recipient pairs. We calculated polygenic risk scores (PRSs) for kidney function-related traits in both donors and recipients. We investigated the association between these PRSs and recipient eGFR at 1- and 5-year post-transplant as well as graft failure. Donor: hypertension PRS (P < 0.001), eGFR PRS (P < 0.001), and intracranial aneurysm PRS (P = 0.01), along with recipient eGFR PRS (P = 0.001) were associated with eGFR at 1-year post-transplantation. Clinical factors explained 25% of the variation in eGFR at 1-year and 13% at 5-year, with PRSs cumulatively adding 1% in both cases. PRSs were not associated with long-term graft survival. We demonstrate a small, but statistically significant association between donor and recipient PRSs and recipient graft function at 1- and 5-year post-transplant. This effect is, at present, unlikely to have clinical application and further research is required to improve PRS performance.