The eyes are the windows to the soul, as they say. If you know the proper cues to look for, you can determine if someone is attracted to you simply by looking into their eyes.
The first signal to look for is eye contact. Specifically, you are trying to see for how long they will maintain eye contact with you, or if they bashfully break away, how many times they establish eye contact again.
Another giveaway is how quickly they blink. Attraction affects the rate of blinking, so what you are looking for is an increase in that rate, meaning more blinks per minute.
Thirdly is a change in the size of their pupils. Eyes dilate and constrict from more than just a response to light. The physical and emotional attraction will both affect pupil size, causing them to dilate.