There are currently no periodicals devoted to the Perl programming language.

Issues of The Perl Journal, which ran from 1996 to 2000, can be found online.
See this interesting comment⤯ by brian d foy for more information about the history and status of TPJ.

Perl Month was a periodical which ran for eleven issues ending in 2003 or earlier. All can be found in the Wayback Machine: primary archive, secondary archive.

There is The Perl Weekly, "a round-up of hand-picked news and articles" about Perl, though it does not produce its own original content.