Development of local P fertilizers using low-grade phosphate rock (PR) is expected to overcome the low-stagnated crop yield in Sub-Saharan Africa. Calcination and partial acidulation methods have been proposed to increase the phosphate (P) solubility of PRs. However, the effects of fertilization with calcinated PR (CPR) and partially acidulated PR (PAPR) on sorghum [Sorghum bicolor (L.)] and cowpea [Vigna unguiculata (L.) Walp.] cultivation are poorly understood. Therefore, we conducted a 2-year field experiment in Burkina Faso to identify the differences in sorghum and cowpea responses to CPR and PAPR application. The following eight treatments were applied with six replicates using a complete randomized block design: control without P fertilization, two types of CP (CPs), triple superphosphate (TSP) as a positive control for CPs, three types of PAPR with different degrees of acidulation (PAPRs), and single superphosphate (SSP) as a positive control for PAPRs. SSP mostly comprised of water-soluble P fraction (WP), TSP and PAPRs of WP and alkaline ammonium citrate-soluble P fraction (SP), and CPRs of SP and 2% citric acid-soluble P fraction (CP). Their solubility was in the order WP > SP > CP. The fertilization effects were evaluated by P use efficiency (PUE). In 2019, the biomass and P uptake of sorghum was decreased by the low available soil water at the early growth stage. On the contrary, cowpea survived the low available soil water because of its shorter growing period compared to sorghum. P fertilization significantly increased the grain yields. However, the effect size differed according to the crop and fertilizer types. The SP, along with WP, significantly contributed to the PUE and grain yield of sorghum, whereas only WP contributed to the PUE of cowpea. Therefore, CPs, mainly consisting of SP and CP, had a disadvantage compared to TSP, especially for cowpea. We thus concluded that PAPRs are effective for sorghum and would be effective for cowpea when the acidulation level is sufficiently high. We also conclude that the long growing period of sorghum is favorable for absorbing slow-release P, but is unfavorable for the variable rainfall often observed in this region.