Check inside your hot tub near the computer controller/ eletric pump area, there should be a small metal plate stamped with the manufacturers minimum amp breaker requirement...likely 50 amps in your case. If your 100 Amp breaker box has the room for a 220 volt GCFI breaker then you should be OK. Most homes under 2.000 square feet have a 100 amp service panel.
Most important of all you must use a GCFI breaker!!! (Ground Circuit Fault Interrupt)
GCFI breakers are quite expensive (usually $150 or more) , however, it's mandatory, as this is required by law to prevent electrocution due to a possible ground fault event. It will trip the breaker at even a hint of ground fault/leakage.
Also, there should be a separate power/switch box (Spa Box) within 10 feet of the Hot tub so as to be able shut the power-off in an emergency.
Check you local city building code for requirements in your area.