Can I still take a shower if my hot water tank is starting to leak

Sure. However you may not have hot water if the flame goes out. Get it fixed before you possibly flood the house.

You MIGHT get away with a HOT shower today, But tomorrows is not promised unless you FIX that leaking hot water heater. Leaks don't fix themselves and get worse, more expensive and possibly dangerous.

I think I would make fixing the leak a priority over today's hot shower. I hate to be caught NAKED with soap in my eyes, if the small leak turns into a rupture.

It will get progressively worse. Deal with it in timely manner before it becomes an emergency

Milo