"Tirar / Lanzar la caña" = To throw the fishing rod*

To seduce. A very plastic image related to fishing. You throw your cane and wait to see whether you are lucky and someone bites your hook. It is normally used when you are on the pull or in a more general context, for anything you may be after.
"No paró de tirarle la caña en toda la noche, pero la chica / el chico no picó"