If you get a warrant in Wisconsin for a misdemeanor drug charge will they arrest you in Illinois and take you to Wisconsin to serve time?

Sentencing is nearly always going to go much better if you show up voluntarily in court and turn yourself in.

I don't know specifically about Wisconsin and Illinois, but in general, you can get arrested based on an out of state warrant, but some states may not bother to extradite you for a misdemeanor.

Added: In this day and age of budget crunches, it may seem unlikely - BUT - where the law is concerned, never say "never!" All US states and territories honor each other's requests for extradition - there are no 'safe-haven' states - It is impossible to know with certainty whether a particular state will choose to extradite you for a particular offense, or not, there are simply too many variables. It may depend, in part, on the offense and the seriousness of it, and/or how badly they want you returned - most states WILL extradite for felony offenses and crimes of violence.