Rui Hachimura made his debut as the Los Angeles Lakers' newest addition on Wednesday ... but a lot of his fans back home missed out on the action -- 'cause the historic moment caused the NBA's streaming service in Japan to crash.

The Lakers acquired the 24-year-old from the Washington Wizards earlier this week ... shipping Kendrick Nunn and a handful of second round picks to secure the deal -- making Rui the first Japanese-born player in Lakers franchise history.

Fans were quick to complain on social media about not being able to watch Rui check in towards the end of the first quarter of the Lakers' home win over the San Antonio Spurs ... forcing the streaming service to address the issue.