A sitting president is immune to arrest by any law enforcement. However I think there are exceptions such as “high crimes & misdemeanors”. Generally speaking, it is almost impossible.
The President is NOT exempt from the law, so he can be legally arrested for the same reasons as any other person in the United States. (The Supreme Court so found in relation to the unpleasantness related to the Bill Clinton). The President’s lawyers argued that he could not be made to testify on a lawsuit while he was President. The Supreme Court decreed otherwise, stating that the President was not exempted from the laws that applied to all citizens.
The practicalities involved may be something else. The President is protected by the Secret Service, and it is not likely that any law officer will be allowed to simply walk up to the President and place him under arrest.
One thing that may be somewhat confusing is that the Constitution protects members of Congress (Representatives and Senators) from arrest while they are on their way to Congress or while performing their duties. The president does not enjoy such protection.