Is there a convention for the ordering of phases in three-phase power in the US?
They sell testers for this purpose starting at &lt; $20- sometimes running in reverse can cause severe damage to machinery. 



I would not trust that the convention was followed even if there is one, in such a case. 

I also cannot recommend the cheap testers, especially on > 240VAC due to potential for arc flash and such like- a real and appropriate CAT number should be present. Something from a reputable maker might be more like $150 (the one shown above is of the former category and is sold on Amazon- meaning that they probably are required to carry enough liability insurance to cover your next of kin).  

Older testers actually had a small 3-phase motor and you would observe the direction of rotation, but newer ones are generally electronic. 



Directly in answer to your question, the color code is listed as "common practice" in the US and "mandatory" in Canada as follows (somewhat unofficial source here):