Sending such a high-level official to the inauguration suggests the White House is still seeking to repair its relationship with Rousseff following spying revelations.
The Brazilian leader was outraged when documents released by National Security Agency leaker Edward Snowden showed the US had been monitoring her communications. The revelations led Rousseff to cancel plans to come to Washington for a rare state visit.
Biden also visited Rousseff earlier this summer while he was in Brazil for the World Cup. The Brazilian president was re-elected in October.