The correct phrase is "an ear." The article "an" is used before words that begin with a vowel sound, while "a" is used before words that begin with a consonant sound.
In the case of "ear," the pronunciation begins with a vowel sound (/i:/ sound). Therefore, you would say "an ear."
Example:
"She whispered into his ear."
Remember, it's the sound that matters, not the actual letter. So, even though "ear" starts with the letter E, which is a vowel, it is the sound that determines the correct article to use.