Plenty of graphics formats use art extension and it is likely at least some can be opened in either Photoshop or Illustrator and saved as .psd files. Since most of .art files known are vector graphics, Illustrator seems to be better choice. However, it is likely you can also find some 3rd party software capable of this conversion.
Convert Various graphic formats to Adobe Photoshop graphics file.
We found 4 software records in the database related to .art to .psd file format conversion.
Microsoft Windows software - convert art to psd on Windows
A powerful vector graphics editor from Adobe
Convert from art file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned art to psd. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
A graphics editor, illustration tool and web design from Xara
Apple macOS / Mac OS X software - convert art to psd on OS X
Mac version of Adobe's vector graphics editor
On-line services software - convert art to psd on web
An online graphics converter and resizer