Can human eye sense magnetic field?

Yes!

According to a study published in the journal of Nature Communications, human retina has sensors of magnets.

Sensing Earth’s magnetic field is clear in migratory birds and some animals. It was believed, previously, that human beings have no sense to magnetic fields but in a recent study, published in Nature Communications, it has been found that human cryptochrome (CRY2) exhibits light dependent magnetosensitivity. Cryptochrome is a type of protein which can sense blue light. CRY2 is present in human eye in large amount.

Scientists have used transgenic approach to check that human CRY2 can function as a magnetosensor in the magnetoreception system of Drosophila and that it does so in a light-dependent manner. In this experiment, Drosophila were allowed fly in a magnetic field and they showed the results which are sensitive to the magnet.

However, they are unclear whether this capability is translated into a downstream biological response in the human retina.

References and Further Reading:

Foley, L. E. et al. (2011). Human cryptochrome exhibits light-dependent magnetosensitivity. Nature Communications.