No, a website of your own is not a requirement for placing an affiliate link.
You can also distribute the link via social media such as Facebook and Instagram. Moreover, you can distribute the link via a mailing list.
However, placing the affiliate link on your own website is recommended, because in this way you can reach larger audiences and target better your customers groups.
Whenever you still have any difficulties or questions feel free to start a chat (right blue button) or contact us at email@example.com.