In order to check if this is an effective method, in March of 1944, a T-34 upper front hull segment (part number 34.29.304) with track links attached was tested at the NIBT proving grounds.
The shooting was done with an armour piercing 75 mm shell fired from a German gun (PaK 40) with the muzzle velocity of 770 m/s.
Trials showed that the front of the hull protected by track links can be penetrated by the German gun from 800 meters, but not from 900 meters. The unprotected part of the hull can be penetrated from 1000 meters, but not from 1100 meters. Therefore, the tracks increase protection by 200 meters.
I deem it sensible to alter the existing spare track transport method on the T-34 and SU-85. I ask you to order the People's Commissariat of Tank Production to move the spare track link holders to the front of the T-34 and SU-85 hull starting on April 15th, 1944."
CAMD RF 38-11355-2548
Of course, not only the Tigers had such protection. Many vehicles had track links attached to them to the front for extra armour, including tracks from other vehicles.
This StuG, for example, is clearly covered in T-34 track links.
Those that could not find nice and wide T-34 tracks had to make do with less.
As is usually the case, no one waited for orders from the top to improvise. Pictures of T-34s using track links as additional armour way before 1944 are not uncommon. The most common way of using them was tucking them into the infantry rails to protect the turret.