I would like to heat up charcoal in my house, so I can pour some oil on it and give my food a BBQ-ish aroma and slight smoky taste. How do I heat a piece of charcoal using induction stove? I suppose it is dangerous for the induction stove.
Induction cooktops generate heat on iron or steel elements. There's no fire involved.
You want to lit a piece of charcoal on fire. That requires a flame. Induction doesn't generate flames, just heat, so you won't be able to light up your charcoal with just that - I'm not even sure the induction will generate enough heat to light your charcoal piece on fire.
I'd recommend a small gas torch, such as those for searing or creme brûlée.
You cannot do this using an induction stove; use any source of flame instead
In a comment you confirmed you were aiming to reproduce a technique in this YouTube video, in which a piece of burning charcoal is placed in a foil cup inside a saucepan containing cooked food, with oil then poured onto the charcoal to generate smoke.
The gas cooker in the video is only used to set the charcoal on fire; you could do the same with any other source of flame (although it might take longer to light). As Luciano mentions in another answer, you will not be able to achieve this with an induction stove.