Extinction Rebellion Scotland members began their protest at the Shell premises on Altens Farm Road at 6.30am on Thursday and said they plan to stay there all day.
The group say they have secured the entrances with lock-on equipment and the main entrance with XR Scotland's big purple boat, named Amal Gous.
They said they plan to shut the building down to disrupt business and hold Shell to account for its role in the climate crisis.
Police said they were called to the scene at around 6.45am on Thursday.
One of the protesters, who gave his name as Paul, 43, from Aberdeenshire, said: ?"If the whole world reaches zero carbon emissions by 2030, we only have a 75% chance of staying below (an increase of) 2C.
"These are terrible odds; and by committing to continued production decades into the future, Shell is literally destroying our future.
"The more successful fossil fuel companies like Shell are, the worse our future is going to be. We have to stop them carrying on as if their product does no harm. "
The purple boat bears the words "The Future You Fear Is Already Here", a reminder that "catastrophic" climate change is already under way across the planet.
The action is part of Rig Rebellion 2.0, a two-week campaign by Extiction Rebellion Scotland targeting the fossil fuel industry and the institutions which support it.
A Shell spokesman said: "The heightened awareness of climate change that we have seen over recent months is a good thing. As a company, we agree that urgent action is needed.
"What will really accelerate change is effective policy, investment in technology innovation and deployment, and changing customer behaviour.
"As we move to a lower-carbon future, we are committed to playing our part, by addressing our own emissions and helping customers to reduce theirs - because we all have a role to play."