This is a good question. So lets see what the dictionary has to say about it.
"A writer is a person who uses written words in different styles and techniques to communicate ideas. Writers produce different forms of literary art and creative writing such as novels, short stories, books, poetry, plays, screenplays, teleplays, songs, and essays as well as other reports and news articles that may be of interest to the public."
So the answer is yes. Poetry is writing in every sense of the word.
You may write poetry, but never fully understood exactly what poetry is, so lets define poetry for you and others who might be curious as to what poetry is.
"Poetry definition, the art of rhythmical composition, written or spoken, for exciting pleasure by beautiful, imaginative, or elevated thoughts."
Poetry in every aspect is probably one of the most beautiful forms of writing.
Writing poetry can be very powerful and therapeutic for the writer as well as the reader. here's a quote that says it well.
"Writing poetry requires the poet to be extremely disciplined with his choice of words and the number of words, to create a sharp and accurate snapshot of what he or she is feeling."
Here's another definition that says it eloquently
"Poetry is a literary work in verse writing of high quality, great beauty, a piece of art, with emotional sincerity or intensity, a graceful expression showing imagination and deep feeling with beautiful and elegant quality. It is a profound insight that enables a poet to idealize reality and to see the things or situations in a particular way, to express his feelings of his own accord and to represent them in such a way as to delight the readers."
So, now you have your answer. If you write just poetry, you are a writer!
I also am a poet, and a novelist. It's wonderful to know that in a writers world we can have it all, and use it to delight our readers through stories and imagery.