An f/2.2 lens has an entrance pupil (the apparent size of the aperture when looking through the centre of the lens) whose diameter is equal to the focal length divided by 2.2
The focal length of the iPhone lens is 4.1mm so the entrance pupil is 1.86mm, which is not difficult to achieve in a small package.
Aside #1: entrance pupil diameters
To be precise referred to the entrance pupil, instead of the "physical aperture" (the whole in the lens barrel where the iris is located) as the important factor is not how large the hole is, but how large it appears to be from the outside world. The Canon 600mm f/4 lens has an entrance pupil that is a whopping 150mm wide! Yet it is located in the middle of the lens where there is clearly no space for a 150mm opening.
So you might read from this that a large entrance pupil lens doesn't have to be physically large, however in order for the aperture to appear to be 150mm wide, the opening at the front of the lens has to be at least 150mm. And if you look at it it's clear this is the case.
Aside #2: phone camera lens design
Having a small f-number like f/2.2 is not only associated with large lenses but expensive lenses also. Whilst f/2 lenses appear on some compacts, they tend to be high end models. So the obvious question is how the iPhone camera achieves a relatively large apertures at a price that is economical for inclusion in a smart phone.
The answer to this question is that the lens is made from aspherical plastic elements. Asphericals made of glass are very expensive to manufacture, however the iPhone lens is so small they can be moulded from plastic, which is cheap but only works for small elements as the plastic would expand/contract too much on heating when scaled up.