I don't know if there is something out there to do that. But I think it will cause confusion more that it would make any visual enhancement ever. A user will not be happy when scrolling down and finds lines just "popup" suddenly, in opposite to normally easing out as a result of scrolling action.
After all, when we speak about a scrollable HTML element with scrollbars visible, a user is aware text might be partially shown and that is normal and needs to be scrolled down to read the remaining. I really would not recommend that.
But for a technical answer, I think you would need to fix the CSS line-height property of that scrolling element, say make it 8px or whatever fits your layout. Then, capture the scroll event and devide the jQuery scrollTop() by that CSS line-height, then check the results: if it have a fraction then that means there is a "partially visible" line. Don't forget aout margin and padding that can cause mistakes when calculating.