I'm putting together a transformer in a box just for hobby stuff and I want to put a fuse on the primary.
Did I understand the values correctly? Sorry for such a basic question!
7.56 VA
Primary: 115V
Secondary: 6.3VCT @ 1.2 Amps
Primary fuse value: 7.56 / 115 = 0.066 -> ~80mA slow blow
Full secondary max: 12.6V @ 0.6A
Center tap max: 6.3V @ 1.2A
How about the losses in the transformer?
The primary current will be much higher than your calculations suggest.
Small transformers are notoriously inefficient. Unfortunately I couldn't find the efficiency of the transformer you're using but it will be similar to any other transformer of a similar power rating. The data sheet linked below says 69% efficiency for a 6V transformer, so assume about 70% for your transformer., so the primary power will be around 14VA, giving a primary current of just over 120mA.
http://www.farnell.com/datasheets/2603262.pdf?_ga=2.104444297.887224271.1527338544-47418993.1417808164As Benta said, the fuse isn't to stop the transformer from being damaged, but to protect against fire and making the fuse double the nominal current is a sensible suggestion, hence 250mA. I wouldn't recommend anything less than a 200mA fuse.
Note that this transformer has a 6.3V secondary, not 12.6V!
What load is the transformer powering? If it's a rectifier and smoothing capacitor, I hope you're aware that the maximum DC current will be around 70% of the secondary's rating.