Does a childs skin color determine if they will be placed in ESL ?

Only if the skin color is linked to an inability to speak fluent English.

No, of course not. Public schools in the US are required to give a home language survey, and then, for students who report speaking another language at home, a test to determine whether support services in English are appropriate. It's a much more complicated issue than most people think. I know, for example, of a family where the father is Cambodian, the mother is Vietnamese- they speak English, but a limited version since both speakers are non-native speakers, and only had limited education in English. Their children don't speak any language other than English, but still need support services in ESL.

BTW, students coming from France, Spain, French-speaking Canada, etc. might also be placed in ESL classes if their English is limited.

it's probably their accent or inability to speak or understand English.