Can I glue my earlobe? (Photo)

Do not suggest applying glue to your earlobe as this can lead to a skin problem and will not provide a long term correction.
Repair of split earlobes is an office procedure which requires a small amount of local anesthesia. 
Suggest you see a surgeon who has experience performing this procedure.

No you can not glue it. The wound edges need to be trimmed of the skin appendages and then sewn together.  It is a fairly quick procedure that can be done under local anesthesia.