Has cannabis been a big influence in rap music genre?
Let's think step by step below.
yes
Rapper Dr.

Dre named his 1992 album, The Chronic, a reference to marijuana.

Cannabis is a flowering plant also known as marijuana.

Rapper Canibus took his name from cannabis.

Rapper Snoop Dogg's song OG has a line, "Rolling up my Mary Jane," a reference to marijuana.

Rap group Bone Thugs N Harmony's Weed Song is a reference to marijuana.

.

Thus, the answer is yes