"I am an officer."
Translation:Jeg er en betjent.
It would indeed sound more natural without the article.
The article is, however, needed in a sentence like "Jeg er en betjent, der kan lide at hjælpe folk."
When betjent is used alone it is a generic policeman. Unlike in english there is a clear distinction between agent and officer. betjent is not used for military personnel but only for civilians.
Until recently I was employed as a rådhusbetjent, simply meaning I worked in a public office (town hall). A prison warden is a fængselsbetjent. Betjent more or less means an employee in a public service, a civil servant, Maybe it is called an officer in other countries, I don't know.
In the army the officer is a soldier of high rank, løjtnant, kaptajn etc. Under the officer rank are underofficers, up to sergent, and above are the højerestående officerer, like colonel (øberst) general etc.
The lowest rank is a "menig" ( I think you call this a private, I know almost nothing about army, let alone in other countries)