I am certain that one can ordained in the Karma Kagyu lineage.
But this is not something to be taken lightly.
It's also true that, in Kalu Rinpoche's centers, so-called "Shangpa Kagyu" three year retreatants take vows for the duration of the retreat, --on a daily basis--but these aren't complete "monastic vows."
Taking Novice Vows is possible. This is usually the first step in ordination. There may also be options to take the full Monastic Vows. Again, these are not given lightly, and are not to be taken lightly. I know many "novices" who gave their vows back, and there are, of course, cases of those who have broken them.
My advice, FWIW, is to obtain, and take, sojong vows, and then re-take these daily for a period, even before one requests Novice vows. Find a Lama who does Nyung Nes, and discuss this with them.
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