Injuries have been Rivers' problem, in Cincinnati and again in New York, but another problem he had in 2012 was that the Giants didn't have an obvious place to play him. His position was the same one Michael Boley was playing in the Giants' defense, so when Boley was on the field they had to use Rivers in something of a utility linebacker role, and he didn't help much.
Boley's gone now, though, and the Giants' linebacking corps has very little experience on it. It's possible Rivers could simply take Boley's place, though it's also possible they're looking at Jacquian Williams for that role. As was the case last year, the Giants appear to be bringing in Rivers to give themselves as many options as possible for solving their annual issues at linebacker.
What they really need is a middle linebacker, as Chase Blackburn seems set on testing the market. Rivers is not that, and it's unclear what the Giants' plans are for that spot if Blackburn leaves. They like Mark Herzlich, but he didn't show much when given a chance to fill in for Blackburn last year. They have shown interest so far in Jasper Brinkley and Rey Maualuga among free-agent linebackers, and it appears as though they'll have some good linebacker options available to them with the 19th pick in next month's draft if they decide they want to go in that direction.
The Giants don't tend to prioritize the linebacker position, though, so I'd think it's likely they'll continue to work to patch it with mid-range options they find on the market for good prices or with some of their young internal inventory. And who knows? If he can stay healthy for a change, maybe Rivers turns out to be part of the 2013 answer.