On paper, certainly.

The Tiger I had an 8.8 cm KwK 36 gun. Penetration of this gun varies depending on the source and success criterion used, for instance the Germans gave it 132 mm of armour penetration at point blank range at 30 degrees, the British gave it a hair under 120, the Soviets gave it 98 mm. Each of those is plenty in order to defeat the frontal armour of even the most well armoured StuG, which was 80 mm thick. Concrete armour was sometimes added, but this had a negligible effect. Depending on the source of the data, the KwK 36 could penetrate this armour from 1500 to 2300 meters (again, with varying percentages of success), so even accounting for the hit not being exactly straight on or terrain aiding in sloping, the StuG can be taken out from a long distance.

Now, the StuG is more interesting. The ultimate form of the StuG had a 7.5 cm Pak 40. According to the same sources, the gun could penetrate up to 110, 100, or 83 mm. As the Tiger's front armour was 100 m thick, this gets a little dicey. According to Soviet data, the front of a Tiger would only be penetrated head on and at very close range, according to German data it could be done at under 500 meters, according to the British the range would have to be under 100 yards at 30 degrees or up to 900 yards head on.

The sides of a Tiger would be more vulnerable at only 82 mm thick. This would make it vulnerable at a distance of just over a kilometer according to German and British data (or nearly 2000 yards under ideal conditions) and over 500 meters according to Soviet data.

However, these are all just calculations. In real life, the quality of German armour could vary significantly, especially when it came to thick plates produced towards the end of the war. The quality of the welding also decreased, and even a nonpenetrating hit could cause structural damage to a tank that would be enough to force the crew to bail out. The British noted that calculations made according to British armour quality would usually be pessimistic, as in reality German armour could be penetrated at much longer ranges. It would not be possible to figure out the true range at which a StuG could penetrate a Tiger tank without practical trials, but those were rarely performed with the enemy's weapon against the enemy's tanks.

Sources:

Canadian Military Headquarters, London (CMHQ), Files Block No. 55 - 5788 slide 3457

Canadian Military Headquarters, London (CMHQ), Files Block No. 55 - 5788 slide 3335

http://tankarchives.blogspot.com/2013/03/penetration.html

BIOS Final Report No. 614 Item No. 18 Welding Design & Fabrication of German Tank Hulls and Turrets

Armour Branch Report on Armour Quality & Vulnerability of Royal Tiger