It depends on where you live. Usually, in many countries, paintball guns fall under the category of airguns. Hence, laws and regulations about firearms don’t apply to them. This means that they are completely legal to carry without any license or permit.
However, In few countries, paintball is considered a firearm. Therefore it will be illegal to possess a paintball gun without a proper permit or license. Moreover, many US states also prohibit the selling of paintball guns to a minor.
Anyways, for the safe side, It is better to check your state or country law before buying a paintball gun.