This is, in fact, as the previous educator has said, not a quote from William Shakespeare at all. Instead, it is a quote from "Bedouin Love Song" by Bayard Taylor, and it was written in the 19th century, some two hundred years (and then some) after Shakespeare's time. Bayard Taylor, in employing the "thee" pronoun, is deliberately evoking earlier writers with the use of this archaism; this was not uncommon during the Victorian period, particularly when writers sought to create atmospheric settings based in other places and times.

A good rule of thumb when we aren't sure whether something is a Shakespeare quote or not is to examine the rhythm of the piece. The rhythm here, as I'm sure you can see, is not iambic pentameter— that is, there are not five stressed beats to the line. While Shakespeare did not always write in iambic pentameter, his verse almost always conformed to this rhythm, so if the rhythm of a piece does not follow this guide, it should be questioned before we call it "Shakespeare."

People tend to take everything they ever hear that sounds romantic or sounds wise and they say that Shakespeare said it.  I do not believe that this is a quote from Shakespeare.  Instead, I believe that it is a quote from a poem called "Bedouin Song" by Bayard Taylor.

I have checked in databases that include all of Shakespeare's plays and poetry and he never wrote those words.  In fact, he never even wrote the words "I love thee."  Strange, huh?

Anyway, I also have a link to the Taylor poem -- check it out.