Is the A-10's cannon effective against tanks?
Well it depends....
It depends on the tank, where you hit it, what angle you hit it, how far the A-10 was from the tank when it fired, and what kind of ammunition was used.
Wikipedia quotes that a GAU-8/A firing the PGU-14/B depleted uranium API ammunition offers the following armor penetration capability.

Armor penetration of Armor-Piercing Incendiary ammunition, BHN-300 RHA, attack angle 30 degrees from vertical:

76 mm at 300 meters
69 mm at 600 m
64 mm at 800 m
59 mm at 1,000 m
55 mm at 1,220 m


Whether that's a declassified spec with all other known values a secret or a realistic representation is unknown. I'd say it sounds reasonable. Tanks tend to have heavy armor on the front and sides but lighter on the top. Certainly the PGU-14/B could defeat armor on APCs and older generation MBTs. Modern MBTs with advanced composite/reactive armor may be more difficult to crack. While it might not be able to penetrate the chobham hull of an M1A2, it can certainly take out fuel tanks, destroy the engine, etc.
Keep in mind that a GAU-8/A can hammer a 5-mil Circle with 70 such rounds with a 1 second burst, provided the pilot has a steady trigger hand. This also can have a cumulative destructive effect on armor plating.
While the gun can be employed against armor, the preferred method is to attack tanks using standoff weapons like the AGM-65 Maverick missile. Getting close enough to tank columns to use the gun can be hazardous, especially if the group has mobile AAA/SAM escorts.