Maybe.
She is more likely to be on the spectrum than Neville Longbottom or Newt Scamander, the other two HP-world characters I've seen floated as possibly Aspie.
She has the social awkwardness and the special interest. She has the stubborn tendency to cling to what she believes is true regardless of anything that might dissuade her. She's a bully-magnet, she tends to say what she thinks with total disregard for how others will perceive her off and sometimes off-putting statements and she cares little for social conventions.
I don't see much evidence of stereotypy, ritual or repetitive behavior, or clumsiness. We don't know much about what she was like when she was little, as she is fourteen when we first encounter her. We don't really know how she is athletically. The only way we'd know is if she were on the Quidditch team, though, as that's the only sport in the books/movies (other than Dean Thomas's obsession with Muggle football). Of course, for any of the symptoms of Autism Spectrum Disorder, we really only have Harry's observations to go on, as nearly everything is written from Harry's pov.
I think this is a possibility. I've always identified with Luna and identified her as my favorite character in the Wizarding World. It is possible that her eccentricity is a combination of being raised by her father (who is even more Aspie-like than Luna herself) and PTSD from seeing her mother blow herself up with experimental Charms. I have no idea how much JKRowling knows about ASD.
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Your neurodiverse (Aspie) score: 141 of 200
Your neurotypical (non-autistic) score: 71 of 200
You are very likely neurodiverse (Aspie)
Official diagnosis: Austism Spectrum Disorder Level One, without learning disability, without speech/language delay; Requiring Support