Whether or not a war between political entities can result from some action is completely political and strategic, and not legal. The specific incident is probably legal, given US and international law regarding military action. Unless the order was self-evidently unlawful there is no possibility of arrest and prosecution under US law, however there might be a framework for legal action by Iran, if e.g. a drone operator were to fall into Iranian hands. The specifics of the order are not generally known, though we know that DoD states that this was due to a presidential order. This article discusses targeted killing from a legal perspective. In the context of war, killing is legal though not entirely unregulated.
There was a failed attempt to sue the US in the case Al-Aulaqi v. Panetta, which involved a targeted killing of a US citizen involved in planning terrorist attacks, a suit which was dismissed. One problem is that the suit "failed to state a 4th Amendment claim", and also failed to state a 5th Amendment due process claim since Al–Aulaqi's deaths was unanticipated. The court notes that a Bivens claim allows damage action against a federal officer for violation of clearly-established constitutional rights. However,
No case has discussed precisely whether a plaintiff can proceed on a
Bivens action that claims deprivation of life without due process
based on the overseas killing by United States officials of a U.S.
citizen deemed to be an active enemy.
In the discussion, the question arises whether special circumstances counsel hesitation (Doe v. Rumsfeld and citations therein), which the Doe court notes would "require a court to delve into the military's policies", and they will not do that lightly. All of this is about US citizens. Soleimani was not a US citizen.