If there is no reward system or incentive available in the company,Should a Manager on his own reward team members?

Yes, a manager can take a call on this but must work towards making a part of organizational framework and policy. Else it may develop certain side effects like leading to dissatisfaction among the members of other team(s) OR / AND in his own team in  long run.

Yes. Positive reinforcement is key to bbuilding a strong team morale and promoting positive results. The rewards neednt be monetory, it can be a simple recognition of the efforts & highlighting the same amongst the employee's peers by the manager.