Not through the Ethernet port.

The Wi-Fi radio-frequency signals are completely incompatible with Ethernet protocols. To connect an external Wi-Fi antenna, you need a router (or access point) with a jack for an external antenna. Some routers have removable antennas; these allow you to connect an external antenna.

You say "have wireless Wifi in the house"? Do you mean "outside" the house?

Or do you think putting an antenna on a non wifi router will change it to wifi? Answer is no.

So if I’m understanding you correctly, you want to setup a wireless bridge so your home network can access the internet via the library’s connection?
You’d need an ethernet router and a wireless access point that can be configured as a bridge, with an external antenna coax connector to hook your outdoor antenna up to.
You’d then need to know the default gateway, IP range, subnet mask, DNS servers etc used by the library and configure your router to use an IP on the library’s range as it’s WAN address and configure it’s gateway to be the library’s gateway address and connect an ethernet cable from the WAN port on the router to the wifi bridge and your client machines to the LAN ports on the router.
Two points though, do you have permission to use the library’s network?
If not, don’t bother as you could get into a lot of trouble for this.
Secondly, you need to check your local regulations on radio transmissions as you’ll find outdoor antennas tend to be much higher gain units than the small antennas packaged with wireless routers and you may very well end up in breach of laws in this way too.