The laws which ban teens from using normal cigarettes also apply to e-cigarettes (electronic); as the laws which ban teens from smoking are actually laws against the use of nicotine by minors (and even e-cigarettes contain nicotine). So the primary law you are violating is use of a controlled substance.
So yes, in theory you could be arrested.
In practice however I believe it would be exceptionally rare.
First it would depend on your local city or township laws, some cities have exceptionally strict behavior laws (I know a town where you can be arrested for swearing...)
What you are most likely to face is the fact that most towns have laws against where you can smoke, and if you break those you would generally only be cited with a fine. However if you were a minor and could not provide ID for the officer to give you the fine they would be allowed to detain you until parental supervision can be contacted. In which case you may be arrested for disorderly conduct (again depending on local laws, some places disorderly conduct is any act that disregards posted signs such as no smoking or simply not being able to provide adequate identification of who you are)
Chances are if you are caught they are just going to give you a warning, however if you do not comply with requests (such as putting it out, providing ID, explaining why you are there without supervision) than they may find some other reason to arrest you. Also, if you are told to dispose of it, be careful and considerate, be sure to use a proper trash receptacle, chances are if you throw it on the ground you may end up with a littering fine or again arrested for disorderly conduct for being a minor not obeying basic laws.
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They can and should get charges placed. Actions are taken for having any form of illegal substances on a school's campus.