The ARCHway service unites the archaeology journal holdings of over 20 UK university, museum and private libraries to create one searchable resource.
Within this resource are a few archaeological journals whose contents have been digitized.
To locate the full-text of a particular periodical that you know has been digitized, choose the entry entitled Journal Locator. Then enter the first few words of the title in the search box entitled Title.

There are links to ARCHway from the following history page in the Repertorium Veterrimarum Societatum Litterariarum (Inventory of the Oldest Scholarly Societies):

Scholarly Societies Project