Shulchan Aruch (OC 66:9) says he should wait at shira chadashah to answer kaddish or kedusha.
Siddur Derech HaChaimwrites more explicitly:
If he was reading shema when the congregation began praying the Amidah, if he can start and finish the Amidah (until Elokay Netzor) before the chazzan reaches kedusha, such that he will be able to say [kedusha] with the congregation, he should pray [now]. If not, he should not pray [now], rather he should wait at shira chadashah.
[...]
And likewise if he knows the congregation will say barchu, and he has not yet heard [the recital of barchu], [...] if he knows he will not be able to finish the Amidah before the congregation will say barchu, he must wait at shira chadashah until he hears barchu.