You would need to see if you ISP can sell you a static IP - it's not always possible. I can't get one from my ISP when working from home, your ISP may be different for example.
However, if it is just you that needs static IP address (i.e. you as the developer/admin as opposed to users in the public), it is only a few clicks of the mouse to update the security rule thru the aws console each time you need elevated access. I do this for several servers running on EC2 which I keep locked down, and when I need to RDP into them, I open up the security groups to just my (dynamic) IP, and remove the rule when I am done - this will work if you only occasionally need access. You could also automate this process using a little scripting and/or lambda function.
Other option that I also do: I have an service that I need to access continually from a static IP - I use an another EC2 instance (with fixed IP) as the whitelist IP for this, and then I connect to that services by first connecting via RDP to the EC2 instance - and the EC2 instance with the fixed IP then accesses the service using its static IP.