You can’t just plug a USB scanner into an Ethernet port, so you need something in between that “shares” the scanner over the network. The usual way is to connect the scanner to a PC and use USB over Ethernet software like USB Network Gate: you install it on the machine with the scanner, share the device there, then connect to it from another PC on the LAN, where it shows up as if it were plugged in locally, so your normal scanning software still works.
If you don’t want to rely on a PC, there are small hardware USB device servers that have USB on one side and Ethernet on the other, and can put the scanner on the network. And if you’re thinking longer term, a scanner or MFP with built-in network support (scan to folder/email) might be cleaner than sharing USB at all. As a quick workaround you can also just leave the scanner plugged into one PC and use Remote Desktop or VNC into that machine to run the scanning app there—less elegant, but it does the job in simple setups.