You'd need a SoC variety of FPGA with a memory controller as I didn't see one in this code base. Putting this in an FPGA seems feasible.
But I see some challenges. It looks like it's a Harvard-architecture core. That means separate buses for data and instructions, which is not common outside of embedded or specialized systems. I'm sure you can setup GCC to work with this, but it would be a project.
You could build (or find) a memory controller that can multiplex separate instruction and data buses to a single memory space... decide data will be in memory range A and instructions in memory range B, and inform the linker where to put code and data.
I'd probably start by downloading whatever free versions of the fpga tools the vender's offer and see if I can synthesize the code with any of the targets and how well it fit. (assuming someone else hasn't posted that info already). If it isn't going to fit in anything supported by the free version of tools, I probably wouldn't go any further with it myself.
Assuming that it did fit, I would switch gears and would build a simulation testbench, and start tinkering to see how it worked as compared to the docs. If it really is strictly harvard, I'd build a bridge to the FPGA's memory controller that could map two buses to a single memory space. If I got that far I'd start working setting up a compiler and linker to map out code and data partitions to that memory space.
At this point you might be ready to build all this and load the FPGA, but you have no peripherals (like ethernet or a vga). I'd consider slaving it to a raspberry pi or something like that. I saw a debug module in the github repo, so that might be a good thing to expose to the raspberry pi. Or pick a simple bus like i2c and use that to get some visibility from the r-pi into the risc-v state and bridge over to the ram.
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Another direction you could take would be to get something like a snickerdoodle. I believe it can boot linux with the arm core in the FPGA, and it has the peripherals you need like ethernet(wifi) and access to an SD card. So the direction I would take there is trying to supplant the ARM core with the RISC-V. So the effort there would be to disable the ARM core, which ought to be straight forward, and build a wrapper around the RISC-V core to be able to talk to the peripherals in place of the ARM.
Given that it's an ARM core, I'm sure all the internal busing is AMBA (AHB/APB/AXI), so it's probably pretty reasonable to try this.