Was the United States punished in any way by the international community for their use of Agent Orange during the Vietnam War?

I believe your question can be broken into two parts:

Was the use of Agent Orange during the Vietnam war a war crime?

If so, was the US ever tried or punished by the international community for that war crime?

In reverse order: the United States doesn't recognize the authority of the International Criminal Court (or really any prior or concurrent legal authority) to prosecute and punish itself or its citizens. While US courts are theoretically charged with enforcing war crime statutes on American Citizens and soldiers, that's a different angle than the one you're asking about. So even if the use of Agent Orange was considered a war-crime, there's no situation where the US would have accepted any international punishment. There's more recent info about this that intrudes on Subreddit rules, so if you're more interested in this, I'd take a look at some recent legal history on this topic.

On the latter question: the consequences of Agent Orange use on a civilian populace wasn't fully known at the time. In fact, Agent Orange was considered to be a necessary tool of war. This is an interesting report constructed by the RAND corporation about the use of Agent Orange and other chemical herbicides. Simply, Agent Orange was used to deny the Viet Cong access to foodstuffs in the South. Obviously, destroying the crops and jungle food sources in South Vietnam was a huge step, as it directly impacted the local allies and, potentially, didn't really hurt the VC. Specifically, as of the publishing of this report, 1967, it was already clear that there would be severe consequences for the local populations:

Page XII, Conclusions Part (1):

Educate the peasant about the effects of the spray on humans. In particular: "Don't eat or drink sprayed food or water. If exposed, (especially children), wash the spray off as quickly as possible." If, as suspected, further analysis indicates that present spray concentrations occasionally may approach lethal levels for the most vulnerable persons (infant and elderly), perhaps reducing concentrations would lessen the chances of persons receiving lethal doses without significantly reducing the spray's effectiveness in destroying crops.

So, it's clear that the US hierarchy is already aware of the potential horror confronting the people of Vietnam. Given the fact that the intentional use of known-human-lethal chemicals on civilian populations could be construed as a war crime, it's fair to say that one could construe the use of Agent Orange as such.

But, of course, there was no international punishment for same because the US declines to recognize the international community vis-à-vis its own actions.