Certanly can. If you break your leg bones in particular, there will be a period of immobilization almost certainly in Plaster of Paris. When the plaster is removed, the muscles tend to be wasted and on starting walking, this may put extra strain on the adjacent large joints, knee or hip, predisposing to arthritis.
Arthritis may not be the cause of you knee problems, as there are many other causes, but I am just answering your question.
You GP will arrange an X-Ray which will give a likely reason for your problems.