Bismihi ta'ala
In Islam circumcision of a male is regarded as a Sunnah, strongly emphasised on, especially at a young age. The specific time that a male should be circumcised, being very mustahab, is on the seventh day after his birth. If parents are not able to do it in this time, then any time after that.
If the male reaches bulugh and has not yet been circumcised, he will be responsible to get it done. In Shi'i jurisprudence, many of our esteemed jurists consider it to be obligatory for a Muslim male to undergo circumcision whenever they can, if they were not circumcised when they were young.
If a male is not circumcised, this will not affect his acts of worship, except for Hajj. If a man wishes to perform his Hajj pilgrimage, one of the obligatory prerequisites is that he must be circumcised in order for his pilgrimage to be valid.
In answering the specific question, being circumcised or performing circumcision is not a necessary condition for converting to Islam or being a Muslim, and he can do it whenever possible, even after converting.
For any male, whether Muslim by birth, or having converted to Islam, who has not undergone the process, they should consider doing it, as there are many religious and physical benefits for it.
In any case, please refer to the specific view of your Marja' taqleed in this regard.
And Allah knows best.
