If it's the Total Communications modem I believe that's 300 baud only.
Since there aren't anymore online services you can dial into for the C64 your best bet would be a dial-up BBS which is very rare.
Check the C64 BBS outpost
, they have a list of active C64 BBSes (not sure how often it's updated) - most are telnet only but I believe there is at least one dial-up BBS in there.
You would also need a terminal program, CCGMS
was the one of the most popular for the C64.
Otherwise that modem from what I remember of its size makes a nice bookend or paperweight.