There've been a bunch, many of which never really got much further than the city limits. I assume you're not referring to those -- or to booster anthems like WPXI's "Stand Up and Tell Them You're From Pittsburgh." A song, incidentally, that is based on a jingle originally developed for a TV station in Detroit.
Of course, Pittsburgh gets a lot of musical shout-outs, frequently in lists of towns compiled to suggest what an ass-kicking country this is. My favorite example is the Charlie Daniels Band's "In America," when Mr. Daniels advises all of America's enemies to "go and lay your hand on a Pittsburgh Steelers fan / and I think you're finally gonna understand." This song, you may recall, was released in the wake of the Iran hostage crisis ... at a time before many fans at Steelers games had mid-level management jobs in finance, as they seem to today.
Sadly, in songs where Pittsburgh features more prominently, it's often as a backdrop to human despair and misery. Take the garage-rock classic "I'm in Pittsburgh and It's Raining," by The Outcasts.
The song begins plausibly enough: "I'm in Pittsburgh and it's raining." But the very next verse reads "sitting in the subway here complaining." Bear in mind that this track was first released in 1966, decades before Pittsburgh even had the T. At least they spelled "Pittsburgh" with an "h."
Predictably enough, the song's narrator is looking to leave town before the end of the verse: Pining away for his lost love, he pledges "Where she goes, that's where I'll follow / Her trail took me down to Chicago."
Similarly, a 1950s pop singer named Guy Mitchell performed a song with the title "Pittsburgh, Pennsylvania," which broke the Top 10 in 1952. The song was arguably ahead of its time, in that it associated the city with bankruptcy. "There's a pawnshop on a corner in Pittsburgh, Pennsylvania" it begins, establishing a backdrop for the lament "I walk up and down 'neath the clock / But I ain't got a thing left to hock." Once again, unrequited love is the issue, establishing the city as a tough place for singles decades before Forbes magazine bothered to weigh in on the matter.
Indeed, Bruce Springsteen stuck Pittsburgh into the title of his song "A Good Man is Hard to Find (Pittsburgh)," even though the city only appears briefly at the song's beginning and end. "It's cloudy out in Pittsburgh / It's raining in Saigon / Snow's falling all across the Michigan line ..." Springsteen has rarely performed the song, and given Springsteen's obvious affection for the city, it's interesting he hasn't written more about the place. His ballad of the collapse of the steel industry is set in Youngstown, for God's sake (though it does mention the Monongahela Valley).
My personal favorite Pittsburgh song, though, is one of the few that actually seems inspired by the city itself. It's an old Woody Guthrie tune called "Pittsburgh Town." Again, it's not exactly going to endear itself to the Chamber of Commerce (though how many Woody Guthrie songs ever have?). The first verse observes that "Pittsburgh Town is a smoky old town / Solid iron from McKeesport down." And it quickly establishes a note of defiance. Punning on the name of one of the city's largest -- and most labor-hostile -- steel firms, Guthrie asked "What did Jones & Laughlin steal now Pittsburgh?" But in the best Guthrie style, the song ends on a note of defiance: "From the Monongahela to the Ohio / They're joining up with the CIO" (a reference to the Congress of Industrial Organizations, one of the forbears of the AFL-CIO.)
Guthrie's song has been covered by Pete Seeger, and more recently by local folk band The NewLanders. In fact, if you're craving some Pittsburgh-themed music, you might seek out a copy of their album Where the Allegheny Flows. The entire album consists of songs that either refer directly to the Pittsburgh area (one song commemorates the Homestead Steel Strike, for example), or refer to industries with a deep Pittsburgh connection, like the coal-mining ballad "Dark as a Dungeon."
Of course, you could just wait for WPXI to offer another out-of-town jingle celebrating hometown pride.