The answer posted in 2016 is incorrect or out of date. The compatible module is the WU-1b according to Nikon USA’s D610 webpage. It's available from B&H for about the same price.
And the D610 is not Nikon’s entry level DSLR. That's the D3000 DX crop frame series, starting about $300. The D610 an FX, full frame model and in a lot of cases, better than the early D4’s (23 vs 16 MP) and it originally was sold around $2000, hardly an “entry level model.”