Not just the English "er" but I suppose also a cognate of the French "eur" or the Spanish "or" etc. To form the noun for a person or thing that does a specific action.
That is usually óir or eoir in Irish - dlíodóir, feirmeoir, uaireadóir, múinteoir.
Obviously "rothar" comes from "roth". Just out of curiosity, what does the "-ar" mean?
My guess is that it’s an adaptation of English “-er”, so that the literal translation of rothar would be “wheeler”.
This sentence seems to answer the question for you; it's called a roth-ar because it's got a wheel on it :P
There is a wheel on the bicycle. Would this have to be "Tá roth ar an rothar ann." ?
Tá an roth ar an rothar - "The wheel is on the bicycle"
Tá roth ar an rothar - "There is a wheel on the bicycle"