Can an ACL (anterior cruciate ligament) be cured without an operation if the ACL has a grade 3 tear?

ACL is classified as an intra-articular ligament. That means the ligament is present inside the joint. Interarticular ligaments as a rule do not heal and have to be created all new. This is called ACL reconstruction and consists of harvesting a less important structure from nearby and fixing it up exactly in the position of the original ACL.
The best next course for you would be an Arthroscopic ACL reconstruction.

If the ligament is completely disrupted (grade 3) and the joint is unstable. Surgery is usually recommended in young or athletic people who engage in sports that involve cutting or pivoting.

A study suggests that ACL reconstruction can at least be a reasonable option for older patients with torn ACLs, especially if they have feelings that their knees buckle or give way with activity. It is a long recovery after surgery, just like it is for high school and college athletes, but it can be a good option for any active patient.

Its usually a good practice to consult with at least 2-3 top doctors before undergoing a surgery.

Grade 3 ACL year in an young active adult having ligament deficiency symptoms must b operated ASAP. All surgeons who are doing arthroscopic ligament reconstruction have seen additional damage like meniscus ( cushion) injury , articular cartilage ( joint grease) damage in conservatively treated ‘ young’ ACL symptomatic knee joints. Damage due to chronic PCL injury is much more severe beco it precipitates arthritis.

No. Grade 3 tear means there is complete tear of your ACL. I also had grade 3 tear and had it surgically operated. Hamstring graft was used in my case. However,, your surgeon will explain you the pros and cons of each graft.

Related: 

• ACL Tear - Effective Treatments & Recovery Programs