Well, you can said:- "Please, look at me" "Look at me straight in the eyes" "Look straight into my eyes"

^ what wallsoft said: "Look me straight in the eyes" is more common. "Look at me straight in the eyes" is fine, but rarely used. "Look at me!" (in an angry tone) has the same meaning as "look at me straight in the eyes"

"Look me straight in the eyes" or Look at me straight in the eyes" or "Look me in the eye". What is your context? If you are a hypnotist and you want the person to concentrate on you maybe its OK. "Look deep into my eyes, look me in the eyes, you are feeling tired.... look at me straight in the eyes...." However, this expression could also be used by an angry parent who is scolding a child and wants the child to raise his/her head and look the person in the eye while they are being lectured. "Look me in the eye while I am talking to you". Very difficult to do - child is scared, intimidated, (some cultures do not raise children to look at adults in the eye - it is like staring and sometimes a sign of aggression). So! In what context do you want to use the expression - Look me in the eye, and tell me!!!

To me it sounds fine. Let's hear a native english speaker :)