I have an Arduino Nano 33 IoT and have used it for a good time now. I was using it when the antenna snapped off. Is there any way to fix it by either an external antenna or some other method? I tried to just hold the antenna in place as I tried to connect to wifi but it failed to connect.
The problem that I see in the photo is that the pads from the PCB are pulled off and attached to the antenna. So now there is nothing to solder the antenna back to.
While it's possible to rework this with some solder rework tools, I suspect you don't have those. There is really not much else you can do but replace the Nano with a new one. You should still be able to use this one for an application that doesn't need WiFi.
It looks like the two active leads (the two in the upper right-hand side of the green module may be those) are still intact. If you have a small tip soldering iron and a steady hand you may be able to put a tiny drop of solder on both of them and then resolder the antenna to them. You could support the antenna with some silicone caulk or other non-conductive adhesive after you get it attached.
Keep in mind, that this is tricky to solder by hand but there is little to lose since that part of the module is not non-functional anyway.