Can a discrimination, e.g. based on gender, race or age, charge be filed by a prosecutor or a prosecutor's office in the US?
"Charge" conventionally refers to a formal accusation of an offense which leads to criminal prosecution. It is a prosecutor who would file such a charge. The next question is whether there are criminal offenses subsumed under the rubric of anti-discrimination laws. There are a lot of anti-discrimination laws: numerous types at the federal, state and municipal level and different domains of discrimination (employment, public accommodation, education, voting...). Anti-discrimination laws generally describe civil consequences resulting from impermissible discrimination, not criminal penalties. 52 USC 10308a, part of the Voting Rights Act of 1965, provides criminal penalties for anyone who (attempts to) deprive any person of any right secured by section 10301-10304 or 10306. 10301 is the provision that people cannot be denied the right to vote on the basis of race of color. That is an example of a form of discrimination that can result in criminal charges, which are filed by a prosecutor. There is a broad class of criminal laws, the hate crime laws, for example it a crime to (threaten to) use force to interfere with housing rights based on race, color, religion, sex, disability, familial status, or national origin: but not age (it would be a different, non-federal crime). In all of these cases, it not bare discrimination, but discrimination in committing a crime.
Civil actions based on violation of anti-discrimination laws are often undertaken by the city attorney, attorney general of a state, or US Department of Justice. They may have various names such as "District Attorney", "State's Attorney", "County Prosecutor", and there isn't a strict segregation between the attorneys who prosecute criminal cases for the government and those who do other kinds of legal work. So a prosecutor would be the lawyer who files a discrimination action against someone.