Divorce doesn't actually exist in the Roman Catholic Church, so the simple answer is No: they can't.
There is annulment, where a marriage ceases to have canonical effect — it is almost as though it had never been (see this answer — it's complicated). Married people who divorce and whose marriage is annulled can marry in church; it's likely that the same applies to ordination. I couldn't find anything in the Code of Canon Law either: it can't cover every eventuality explicitly, but see below.
Without an annulment, the man is still canonically married and cannot be ordained priest: see Canon 1042(1). Following ordination, they cannot marry and remain in orders; I know someone who relinquished his orders in order to marry. Even deacons cannot marry after ordination — they take a vow of chastity on ordination; but if they are already married they can be ordained deacon.
There are a few married priests in the Church, but they have to have had individual permission from Rome to be ordained (Canon 1047(2)(3)), and if their marriage ends (by annulment or widowing) they cannot remarry. The same applies to married deacons: they cannot remarry while in orders.
There is an interesting supplementary question about annulment which arises though. Imperfect intent is grounds for annulment — that is, if one of the parties never really intended the marriage to be a real marriage, then the Church can annul it. If a man contracts marriage but never intended it to last because he felt called to ordained ministry, would that be valid grounds for annulment, and if so, could he still be ordained?
It seems it may well be valid grounds for annulment because of the lack of good intent. However I guess that from the statement in Paragraph 72 of ARCIC's document Life in Christ, the Church might consider that serious psychological defects exist. In that case Canon 1041(1) provides a reason not to proceed with ordination.
This might even obtain for a man whose marriage ended in annulment through no fault of his own.