'12 CTS Performance Sports Wagon AWD
That is one of your PCV lines. They are very brittle and can break easily. That looks like the one that comes from the passenger side head. You likely have a line exactly like that one on the passenger side of the intake and the two come together before it goes to the passenger side head. My 2009 Sedan looked just like that. The 2012 has 1 single line and it goes into the top of the intake. You also have a similar line that goes from the back of the drivers side head to your intake hose. You can replace the line with 3/8 fuel line and it should work fine. Or just stick some over that plastic line but you may have other sections of it broken. I had to replace those lines on both of my cars. I have all 3/8 fuel line on mine now going to a Tracy Lewis Oil Catch can.