Can I glue the float back onto linkage to my toilet fill valve?
That whole assembly is the toilet tank fill valve. The float assembly below rises as the tank fills and pushes up the tab that broke. That in turn pushes up the linkage rod and then the lever to turn the water off. I am not sure what made the tab on the float break but possibly the plastic just got super brittle after being exposed to chlorine in the water over a long period of time.

I do not think that a simple gluing of that tab is going to last. The types of plastic used for these do not lend well to being glued. And if you did get some glue to hold initially the exposure to water could make it fail. 

Replace the whole toilet fill valve. They are not that expensive [mostly due to being made of all plastic parts  :-) ] at your big box home improvement store. The last one I purchased was between 10-12USD.