Though most people do get surgery to reconstruct their torn ACL, it is possible to regain full ability of your knee without surgery. Just through rehabilitation, you can totally recover from a torn ACL.
In a clinical trial done in 2010,1 two different treatment strategies were given to 121 young, active adults (ages 18-35) who suffered acute ACL injuries. One strategy was rehabilitation with early ACL reconstruction surgery. Most people given this treatment strategy opted for the early surgery (61 out 62). The other strategy was rehabilitation with delayed ACL reconstruction surgery. Of the 59 people treated with this strategy, only 26 people opted to get surgery. The other 36 were healed with just rehabilitation.
Though that trial was meant to find the most effective treatment of torn ACLs, it did display that with physical therapy and time, it is possible to completely recover from a major ACL injury.
There are some situations in which rehabilitation without surgical reconstruction is not very effective for a torn ACL. If other parts of the knee, such as other ligaments, have also been injured, it is recommended that you get surgery. It is also recommended that you get surgery if you are still active, as running, jumping, pivoting, and other activities that give you a higher chance of reinjuring your ACL.
1: A Randomized Trial of Treatment for Acute Anterior Cruciate Ligament Tears
MedicineNet: What is the treatment for a torn ACL?
Sutter Health: Nonsurgical Treatment for ACL Injuries