Yes and no.
Technically, any person who is licensed to practice law can represent an injured construction worker.
However, you need to exercise extreme caution when choosing a lawyer for your case. Construction technology is intricate, so it is important to be represented by an attorney who has knowledge of construction methods and construction safety regulations. Your attorney must be versed in OSHA and ANSI and other safety regulations, and must be knowledgeable about standard construction documents.
It has happened often that an attorney with no experience in construction site accidents will decide to file a lawsuit on a client's behalf. This can prove disastrous, because, without the advantage of knowledgeable economic analysis of the case, the attorney may not realize that the costs of the lawsuit are going to exceed the amount that can be recovered for the client! Sometimes the best legal advice is not to file a lawsuit.