Can I use the phrase "black man" in a story without being thought of as a racist?

If the guy who refers to the black man as a black man doesn’t know any other terms, then I’m pretty sure it’s acceptable. In fact all terms are acceptable, unless obviously racist words like ’‘nigger’’ get used, and even then, you might have a racist character in your story, doesn’t make the writer racist.
Given the idea in your story here, I don’t think anyone is going to think you or the story is racist. There are a lot of stories out there that use derogatory words for people from different places, and stories that are about racism, yet most readers don’t interpret this as the author being racist, or the story delivering some infamy on the matter.
I think the words black man are safe. :/

I can’t defend my opinion as anything but my opinion, but I agree with @Symbeline. I also think it’s much more tasteful and less risky just to say he’s a black man than to try for some kind of coy indirection, inviting the reader to make an inference from adding up physical characteristics. How are you describing the other characters? Are you calling them white men?

I have to add, though, that if the man’s race is important to the story, perhaps it can be shown within whatever context makes it important. And if it isn’t, then why mention it at all?

I think it just depends on if you want to give your character volume and depth or if his is just a Black man. If the character is just passing through the then can stick with just a black man. it would detach him from the story and give him less personality.
Ex. A black man walked in the room wearing a nice coat.
A dark skinned man walked in the room wearing a fine silk suit jacket.
A n****r walked in be-boping and pants saggin.
Basicly, my point is that is all about how you want to develope your character, and the implementation of context clues. As a writer its up to you to develope your story as you want you audience to read it.

Not that I have 100’s of black friends, but the ones I do have seem to prefer being called “black” over any other kind of description.

Based on that, I would say it is not racist.

I don’t get offended if anyone calls me white so I can’t see what anyone would be offended to be called black. In Australia the aboriginal people refer to themselves as blackfellas and whites are whitefellas.

If knowing the race of the man coming in is important to the story, I would describe him as black. If it wasn’t important to the story I would not mention his race at all.

The guy has probably looked in a mirror and realized he’s black, so I doubt calling him black would be racist.

It’s best to call a spade a spade, that’s what I was always told.
Any racist overtones found in that innocent remark lie purely in the mind of the reader.

Sure. I know very few people – even among blacks, with whom I work closely – who actually use “African-American.”
I like @Jeruba‘s and @WestRiverrat‘s answers, too.

YES.

It is your right as a sovereign individual to choose how many syllables you use to describe something.

A word of advice: Life is far too short to entertain petty concerns such as this one.

Don’t be so obsessed with how others see you, you’ll be surprised by the amount of respect you earn.

I think it would derive a connotation by the sentence it is placed in. Perhaps the other man is racist, in the story I mean. It’s strange to read this since I live in one of the most supposed racial countries in the world. We would just say black man, white man and no one would bother.

Black is beautiful!

Depends on usage/context, but it’s probably as innocuous as “blond woman” or “tall man”

@WestRiverrat, isn’t that exactly what I said? ^^^

no

I only asked because I was curious as to the discussion that would result and if I thought such a discussion of thoughts would result in the mind of the reader, adding a layer to the story. It is important in a way to describe him as such rather than using a phrase like “he walked on the luxurious red carpet across the office and sat down in the rainbow colored bean bag” or “The pale woman was beside herself when the makeup counter saleswoman suggested more rouge”. It adds depth to the personality of the old man I feel to see how he sees the young man.

My opinion is using black man is fine. I still use black man/woman/person. Most people I know prefer black to African-American. I had a very white, blond, blue eyed former neighbor who was African, came to America when she was a teenager from South Africa.

Wait @JLeslie, you were neighbors with Charlize Theron? Whoa.

All of the responses have been very much appreciated. I thank you.

@ZAGWRITER She checked the box African American when trying to get her son into a magnet public school that admitted children by lottery, but there was a quota of spaces set aside for minority kids and the area is extremely white. LOL. In the end she put him in a private school so nothing came of it, but it would have been interesting if her blond caucasian boy did get in because of how she filled out the application.

Fascinating! I love finding out interesting stories and things because I make an amusing (I admit, probably only to me), offhanded comment to someone.

Race has no proper purpose on an application of any kind.