Hello,
The Qur'an itself states that only those who are clean and pure should touch the sacred text: "This is indeed a Holy Qur'an, in a book well-guarded, which none shall touch but those who are clean..." (56:77-79). The Arabic word translated here as "clean" is mutahiroon, a word that is also sometimes translated as "purified". Some argue that this purity or cleanliness is of the heart, i.e. that only Muslim believers should handle the Qur'an. However, the majority of Islamic scholars interpret these verses to also refer to a physical cleanliness or purity, which is attained by making formal ablutions (wudu).
A non-Muslim should not handle the sacred text, but may listen to tapes of the Qur'an or handle a translation. (If you cannot perform wudu)
There is no restriction on who can and can't read the Qur'an it was written for all of humanity,
Allah says, "And we have indeed made the Quran easy to understand and remember."
Allahu Alim (Allah knows best)
Peace be upon those who follow guidance.