- immersion in a mikvah
- bringing a burnt offering
The Rambam continues and tells us that nowadays, when there is no Temple, circumcision and immersion are performed, while the burnt offering is only brought when the Temple is rebuilt.
There are several places in the Talmud that tell us that when one learns about a sacrifice or reads the Torah portion that talks about a sacrifice, G-d considers it as if one has offered that sacrifice. See for example Menachos 110A and Taanis 27b.
Why is there no obligation for the convert to read/learn the Torah portion that talks about the Korban he must bring? Even if reading/learning that portion is only partially as effective as actually bringing the sacrifice (as the Beit Yosef (Orach Chaim 1, d"h VeAchar Parshat) says regarding a Sin Offering - see an examination of this here), it still seems to me that it is still better than nothing, at least until the actual sacrifice can be brought.