Up to 14,000 people could lose their jobs.
The firm said lower demand and higher costs had made the pits unprofitable.
It sacked 12,000 workers last year during a strike over wages, claiming that weeks of illegal strikes had cost it £50 million.
The workers were reinstated following union negotiations, but today Anglo American announced a restructing plan in light of "structural changes" in the industry.
It hopes to cut £270 billion by 2015.
This could affect 14,000 jobs, 13,000 of them at Rustenburg.
Chief executive Chris Griffith claimed it was "not a reprisal against the strikes."
But miners' spokesman Evans Ramogka warned of a strike across all its operations if the pits are closed.
"If they put any shaft on care and maintenance, all of the operations will go on strike.
"Nothing like this will be allowed."