Gerim can get semicha. There is a rule, however, against a ger having a position of communal authority (not sure of the origin though). I’m not sure, but the reason for this law may be that having a ger as a leader may make the community feel uneasy or suspicious, and the ger himself will notice and it will be an unpleasant experience (since gerim are more sensitive). However, I’m not sure how strictly this is applied in practice. For example, I think the Chief Rabbi of the Czech Republic is a ger.
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