Hi.
Yes, you need to provide your card details to get the 60-day free trial.
However, if you cancel your subscription before the 60 days, for example, on day 59, you won’t be charged.
If you have doubts about the free trial, I recommend contacting the Digital Ocean support directly, they will provide more detailed information.

There’s also some more information from their FAQ:

Are there any limitations with the free trial?
The $200, 60-day free trial provides free credit up to $200 that must be used within 60 days. If you go over $200 in infrastructure services during the 60-day period, any overage charges will be charged to your credit card.
After 60 days, any active infrastructure services running on your account will be charged at the standard pricing.

How do I sign up for the free trial?
If you are eligible, your free trial will start when you sign up for DigitalOcean. You will need a credit card so that we can verify your identity, but you will not be charged or billed during your free trial.

Who is eligible for the free trial?
New customers to DigitalOcean with a valid credit card are eligible. You are eligible if you have never been a paying customer of DigitalOcean and have not previously signed up for the free trial.

https://randomnerdtutorials.com/digitalocean

I hope this helps.
Regards,
Sara