Dropbox has no functionality for mapping a drive to your account.
They do have a SmartSync feature that allows you to specify that folders within your account are only accessible online (not stored locally), but this feature is only available to Dropbox for Business/Enterprise accounts.
OneDrive, if you're on Windows. There are also third-party utilities that will allow you to map a drive to various cloud storage providers (including Dropbox), but they're typically slow and cumbersome, and rarely supported by the storage providers. I've even heard of problems with the feature on OneDrive, and it's Microsoft's own product.