Apple Pencil won't connect to my Apple iPad mini

First, compatibility. Verify that your Apple Pencil is compatible with your iPad:

Apple Pencil compatibility - Apple Support

Assuming that you have an Apple Pencil that is compatible with your iPad, this support page may be helpful with pairing and use of the Pencil with your iPad:

Connect Apple Pencil with your iPad - Apple Support

If you continue to experience difficulties, here is one of the better troubleshooting guides:

https://appletoolbox.com/apple-pencil-not-working-heres-our-troubleshooting-guide/

Be aware that if your Pencil has been set-aside for an extended period, unused and uncharged, the Pencil battery may now be irretrievably damaged through deep discharge. In common with all Li-ion batteries, they must always have some level of charge.

The tiny internal Li-ion battery is susceptible to permanent/irreversible damage through being left discharged for long periods. Even some “new” pencils can exhibit signs of failure out-of-the-box if they are “old stock”. 

It is essential that if you have an Apple Pencil that you charge it regularly - whether used or not - so as to protect the battery from deep-discharge. Do not allow a pencil to remain in low-charge state for any period of time - as the internal battery will fail, rendering the Pencil useless. Setting aside an unused Pencil, for extended periods, is a recipe for premature death of the Pencil battery.

If the Pencil Battery has failed, the only remedy is to replace the Pencil. If the battery has failed and your pencil is within its one-year warranty, you should look to having it replaced by your retailer or at an Apple Store.

A second generation Apple Pencil should be kept docked with the iPad when not in active use - as this ensures that the tiny internal battery is kept optimally charged when not in use. Charging only occurs when the battery requires charge from the iPad, optimal charge being entirely automatic.

Keeping the Pencil separated from the iPad when unused risks allowing its battery to discharge; if allowed to remain in this state, the battery will suffer irreparable damage. When the battery fails, the only remedy is to replace the entire Pencil; the battery is not a serviceable item.

The first thing is to check to see if you have the correct pencil.

I believe you need the 2nd generation pencil.

Apple Pencil compatibility - Apple Support

The pencil needs to be charged all the time. If the pencil has been laying around a while with out being charged the very tiny battery may have failed.