The glass is already broken (or no water would have been able to get in). The break may seal at room temperature, and open up when the glass is heated.
To test this:
- Take a vessel that's larger than the cup, and fill this with hot water.
- Submerge the glass in the water, and see if water leaks in.
If water leaks in, the next step is to find the leak. If you examine the glass under a bright light, you may be able to see the crack.
Then leave the glass with the crack pointing down. If you keep the glass hot, the crack may open enough to allow the water to drain out.
You can try applying glass glue on the crack, but I don't see that holding very well. The glue should really be applied on the edges you want to glue together, not on the outside surface of the crack.
It's unlikely a repair will hold long, and (due to the uneven stress on the glass when it's used with hot liquid) chances are the glass will break completely if you use it again.