Yes, Statoil of Norway has been doing this for a long time link:

About 2,800 tonnes of carbon dioxide are separated daily from Sleipner West's gas production and injected into the Utsira sandstone formation (aquifer), rather than released to the air.

This solution has been in use since the field came on stream in the autumn of 1996. But 2000 is when the saline aquifer carbon dioxide storage (Sacs) project demonstrated that the injected gas remains in place rather than leaking out.
...
With a thickness of 250 metres, the formation can store 600 billion tonnes of carbon dioxide. That compares with a mere million tonnes being injected annually from Sleipner West.

"The entire carbon dioxide emissions from all the power stations in Europe could be deposited in this structure for 600 years," says Mr Torp.
...
Mr Torp admits that the researchers cannot promise it will stay in store for ever. But a duration until the next ice age, in 5-10,000 years, must be good enough, he says.

Statoil will also separate and reinject the CO2 from its new Snovhit field