Is it acceptable to begin a declarative sentence with "Am"?

Some languages are subject-drop languages, but English is considered a subject-obligatory language. The sentence as it stands is non standard. It's the type of telegraphic language you might see in a text message.

There is a style of English speaking which drops subject pronouns, which I associate (perhaps wrongly) with Colonel Blimp-type figures. Something like:

Went up to town this morning. Met Caruthers at the club. Just got back from Africa. Ate a well lubricated lunch together for old times' sake. Am now coming home by train.

It is not standard English, and is prone to ambiguity. But it exists.

It’s quite normal to drop the subject pronoun in contexts where brevity is important. It is certainly a practice found in emails and texting, but it was previously found in their predecessor, the telegram, and many people drop the subject pronoun when taking notes. It is also dropped in quite formal prose to avoid repetition, as in, for example, I went to New York last week and am going again tomorrow. It is a form of ellipsis, and should not be considered ungrammatical.