Betting sites accept the most common Visa, MasterCard, Skrill, Neteller, paysafe, pay by mobile, as well as country-specific payment methods such as giropay, Euteller, Klarna, etc.
Keep in mind that the regulators in some countries are taking serious measures to curb gambling through international betting sites and you may stumble upon deposit and withdrawal restrictions. In the UK, for example, credit card deposits are prohibited across all gaming verticals. There is also a huge number of countries where withdrawals to a MasterCard are not allowed.