Candle wicks used to have lead cores. But studies revealed that lead in the candle wicks was being released into the air in the candle smoke. So, the National Candle Association worked with its member manufacturers to voluntarily discontinue using lead wicks as early as the mid-1970s, and in 2000, asked all U.S. candle manufacturers to join its members in signing a formal pledge not to use lead wicks. Lead wicks were officially banned from the U.S marketplace in 2003, and were voluntarily pulled from the market even before that.
Nowadays, the cores are made of zinc, paper, tin or cotton, with cotton fibers woven around them. Scientific studies have repeatedly shown both zinc-core and tin-core wicks to be safe and non-toxic.
While pretty improbable, it's still possible that cheap candles made overseas may contain lead in the wicks. All the more reason to make your own candles using wicks from reputable candle making suppliers - or at least buy your candles from a reliable vendor. Don't be afraid to ask the salesperson or vendor if they know for certain that their candles' wicks contain no lead.