Did Lord Shiva smoke weed?

Weed is godly. Weed is ungodly.
Take your pick. I choose both.

Former needs significance; latter needs both justification and significance to understand the answer to the question Why does Lord Shiva smoke weed?

Weed is ungodly.
Considering this point of view, ISKCON volunteer S. D. Adhikari gives a beautiful explanation

"Just as the sun is so powerful it can extract water from urine without being polluted, Lord Shiva is so powerful that he can swallow an ocean of poison without being harmed. Similarly, he can smoke marijuana without losing his stature"

Further he adds

"To know why he smokes it is not very important. The important thing to know is that he can smoke it, while we cannot."

However he provides no information for "Why Shiva smokes weed?"

Weed is godly.
Weed is illegal, how can it be godly?
Here is the answer. According to The Vedas, Marijuana having numerous medical benefits was one of five sacred plants. Given that studies across the world show that moderate consumption of marijuana is far less harmful than tobacco or alcohol, it makes little sense to uphold the ban on its recreational use. Unfortunately due to western pressure/influence in India Marijuana is banned.

Question remains unanswered "Why Shiva smokes weed?"

Aghoris are devotees of Shiva manifested as Bhairava. Read Why do Aghoris consume marijuana at some holy shrines? How is it linked with spirituality?

Long story short, Aghoris are yogis and Shiva is the ultimate yogi. Marijuana helps them concentrate on the strenuous yogic practices.