Just like it is with all divers, the individual health of the person must be taken into account before determining whether scuba diving is a safe option for that individual or not.
An asthma patient may be at a higher risk of injuries but that can also be the case with any other individual who has a relatively poor physical shape. In case your health is good overall and stress is not a major trigger for you, diving can be an activity that you can enjoy without any fear.