I have been using dropbox for linux on my workstation with centos 7. However, recently, dropbox requires fedora 21, but my fedora version is 19. Is there any way to update fedora on centos 7? Or I just give up using dropbox?
If you are getting that information from this page: https://www.dropbox.com/install-linux then that just means that the Dropbox package was designed for Fedora 21 (or Ubuntu 14.04). CentOS 7 is derived from RHEL 7 which is derived from Fedora 19/20. CentOS (and RHEL) have both been updated to the minor release versions of 7.6 so any of the needed components such as libraries are there.
You don't need to upgrade your "Fedora version". What you are seeing just means that your version of CentOS was derived from that particular version of Fedora. I've installed Dropbox on CentOS 7 and RHEL 7 and it works with no issues just as yours is working. It even works on CentOS 6 and RHEL 6 even though they are derived from older versions of Fedora.