Possible, yes. As others mentioned, wired is always better, but you could use the 2nd router (assuming it has the necessary functionality/options) in wireless bridge mode to accomplish what you want.

You may also be able to use MOCA adapters instead of a wireless bridge, depending on your needs. MOCA would connect an ethernet port on each router into a nearby coax jack in your home, and then you can bridge the second router that way without needing to do the bridge wirelessly.