There is nothing web-based that operates on a RootsMagic database file.
Could you accomplish your ends through FamilySearch Family Tree? You can edit people in FSFT, match them in RootsMagic and move data between the two. Other people may also edit those people.
Otherwise, you are stuck with GEDCOM as a transfer mechanism between RM and some web-based application or service. You can upload and download with Ancestry.com, MyHeritage.com and other subscription-based services. As for an application, have a look at the Wikipedia page Comparison of web-based genealogy software for those listed as having the "Recording" feature. Any of these will have some collaboration capability.
You have not explained your purpose but you may also want to consider remote control of RootsMagic and file sharing.
Tom user of RM7230 FTM2017 Ancestry.ca FamilySearch.org FindMyPast.com
wiki, exploiting the database in special ways >>> app, a growing bundle of RootsMagic utilities.