Do international students who are J visa have to get health insurance first, before getting J visa? Or the students can have health insurance after they get into US?
tl;dr - Ask your university (or other J-1 sponsor).
The US Department of State requires the J-1 sponsor to enforce the insurance requirements. Your J-1 sponsor may require you to get insurance ahead of time, or may allow you to get insurance immediately upon arrival.
If you want to use your existing insurance, you should still check with your J-1 sponsor. Your sponsor should accept your existing insurance if it meets the coverage requirements listed in the regulations at 22 CFR 62.14. If your insurance meets all requirements except for evacuation and repatriation, you may be able to get supplemental insurance just for those (see Where to buy US repatriation and evacuation insurance only?).
Participants and any J-2 dependents (spouses and minor unmarried children under the age 21) accompanying them are required to carry medical insurance at the minimum benefit levels stated in the program regulations. Program sponsors are required to ensure that all participants have the appropriate medical insurance. Sponsors will verify that the participant's medical insurance meets the regulatory requirements, and will facilitate the purchase of coverage for participants who do not have their own insurance, or whose coverage does not meet the requirements. Participants interested in obtaining appropriate medical insurance should contact the responsible officer of their sponsor organization sponsoring their program. Willful failure on the part of the participant and/or any J-2 dependents to maintain active insurance coverage is grounds for termination from the program. Please refer to the regulations for details. [22 CFR 62.14]
See also: US Department of State Info for J-1 sponsors (click 'Insurance')