Dzigarkhanyan worked as assistant cameraman at Armenfilm studios in 1953-1954. He began his acting career in 1955 at the Russian Stanislavsky Theater in Yerevan, and in 1967 moved to the Lenkom Theatre in Moscow.
In 1969 he joined the Mayakovsky Academic Theater. Dzhigarkhanyan was awarded the Armenian Republican State Prize in 1975 for Triangle and again in 1979 for Snow in Mourning. He appeared as a chief gangster in the 1979 TV series The Meeting Place Cannot Be Changed, playing opposite Vladimir Vysotsky's police investigator.
Dzigarkhanyan was given the title of People's Artist of the USSR in 1985.
He has filmed in more than 170 films(imdb).