I agree with Jesse: these phrases do not have the same meaning. If you rope someone in to do something, you enlist them to help or participate. The person in question may be willing to take part, and the outcome may well be positive. For example, "I'm not free on Saturday. Jack has roped me in to help out with his party. I don't mind, actually. I'll get some free food and drink, at least". Dragging someone into a situation means that you are involving them in something unpleasant against their will, and the outcome is negative. For example, "Leave me out of this! I don't want to be dragged into your arguments. It's nothing to do with me."

You would say: rope me into something. But overall - pretty much the same thing.

"Drag" is a stronger verb than "rope". You are "dragged" into doing something you REALLY didn't want to do, whereas you can be "roped" into something you didn't choose but are still willing to take part in.