The New York City school system is having great difficulty finding teachers to take available jobs, the Board of Education's personnel director, Frank Arricale, said yesterday.

"I want to red-flag this situation before it gets worse," said Frank Arricale, who said that 800 teachers are needed before the new semester begins Feb. 1 to fill vacancies and that another 1,200 are needed if teachers who have applied for sabbaticals are to have them.

Arricale said teachers are abandoning the profession because of a lack of job security, competition from private business, criticism of teachers for all the failures of students to learn and violence in the schools.

"It's become increasingly difficult since September to get people to teach in our system," Arricale said. There have been shortages of high school and junior high school mathematics and science teachers for several years, but now other specialties are also hard to find, he said.

The teacher layoff that followed the city's fiscal crisis in 1975 "shattered the tradition" that teaching had absolute job security, Arricale said.

"Laidoff teachers or teacher candidates found the antiseptic atmosphere of the ivory tower private corporations more pleasant than the nitty-gritty of the schools," Arricale said. Teachers, he added, more than anyone else except firefighters, "have borne the burden of the social problems of the city."

The Board of Education went through a list of 17,500 teachers who had been laid off when teacher replacements were being sought last August and September, school officials said. About 12,000 were no longer interested in a teaching career, they said.

Arricale said that violence in schools had "very little" to do with his problem, but could not completely ignored. The Board of Education reported 2,402 assaults in schools last year - most of them assaults by students against other students.

New York City is attempting to recruit teachers in "the highways and byways," Arricale said. The city requires a special qualifying examination in addition to New York State certification.

A beginning teacher earns $9,200 a year, which increases in 14 steps to $20,000 over 7 1/ 2 years.