Okay, let's put it to the test.
Arrest Barack Obama for the premeditated murder of Abdulrahman al-Awlaki, a US Citizen, with a drone strike on August 26, 2011.

On what grounds?

Obama didn't personally kill al-Awlaki, obviously - which makes a premeditated murder charge all-but-impossible (there are a few exceptions that would allow a person other than the actual killer to be charged, but none relevant here).

You might try to build a conspiracy to commit murder charge, but there's no indication that Obama ever knew about or authorized the killing of al-Awlaki. The criticism against Obama was that the policy of drone strikes and a kill list led to al-Awlaki's death, and as the Executive any terrible policy redounds to the detriment of the President. But there wasn't ever any indication that I'm aware of that Obama was individually involved in, or even aware of, that killing. He wasn't one of the officials named in the lawsuit filed by the relatives against the government over the death, nor did that suit have any allegations that he was involved with or aware of the order to strike al-Awlaki:

ccrjustice.org - July Nasser Al Aulaqi Complaint

Given that, Obama almost certainly couldn't even be charged with a crime, even if the statute of limitations hadn't run out ages ago.