You can if your waive is ready

You can change your status from J-1 to F1 or H1 if your waiver is finished. My friend did that two months ago (J1 to F1). Otherwise you will have to go out for your visa.
Talk with ISO in your school. They will give your a sheet listing on the required documents for your status adjust. The waiver is recommended but actually it is required if you want to change your status from J in US.