You can craft a fishing rod in Project Zomboid with a sturdy stick or find and loot one from a hardware store or backyard shed.
Crafting Fishing Rod
If you aren’t able to loot a Fishing Rod you can craft one. You will need to have the Fisherman occupation, Angler trait or have read the Angler USA Magazine Vol. 1.
To craft a fishing rod you will need a knife (even a kitchen knife works), a sturdy stick, 2x twine/fishing line and 1x nails/paperclip.
Sturdy Sticks themselves can be crafted with a Plank and a Saw. Planks can be obtained from disassembling furniture or cutting them from Logs with a saw (Logs can be cut from trees using an Axe).
Once you have the required items just right click the sturdy stick and select “Make Fishing Rod”. Alternatively you can also use the crafting menu Fishing tab.