Soft-processors implemented on SRAM-based FPGAs are increasingly being adopted in on-board computing for space and avionics applications due to their flexibility and ease of integration. However, efficient component-level protection techniques for these processors against radiation-induced upsets are necessary otherwise as system failures could manifest. A register file is one of the critical structures that stores vital information the processor uses related to user computations and program execution. In this paper, we present a fault tolerance technique for the register file of a microprocessor implemented in Xilinx SRAM-based FPGAs. The proposed scheme leverages the inherent implementation redundancy created by the FPGA design automation tools when mapping the register file to on-chip distributed memory. A parity-based error detection and switching logic are added for fault masking against single-bit errors. The proposed scheme has been implemented and evaluated in lowRISC, a RISC-V ISA soft-processor implementation. The effectiveness of the proposed scheme was tested using fault injection. The fault masking overhead required in terms of FPGA resources was much lower than a traditional Triple Modular Redundancy protection. Therefore, the proposed scheme is an interesting option to protect the register file of soft processors that are implemented in Xilinx FPGAs.