Many graphics file types actually feature .art extension, so it's difficult to give a clear answer as to how to best achieve art to ai conversion, especially in case if you do not know from which software your ART file originates.
Many of these .art files are vector graphics and quiet few of these are actually supported in Illustrator directly, so this presents probably the best way how to do this.
If you do not have access to Illustrator, you will have probably difficult time finding software that not only can import your specific ART format, but supports Illustrator's formats as well. You can always try to do some creative import/export with common vector graphics exchange format, for example SVG.
Updated: September 19, 2023