In his lecture here, he says:
One word more: I read in the organ of the social reformers that I am called a Shudra and am challenged as to what right a Shudra has to become a Sannyasin. To which I reply: I trace my descent to one at whose feet every Brahmin lays flowers when he utters the words — यमाय धर्मराजाय चित्रगुप्ताय वै नमः — and whose descendants are the purest of Kshatriyas. If you believe in your mythology or your Paurânika scriptures, let these so-called reformers know that my caste, apart from other services in the past, ruled half of India for centuries. If my caste is left out of consideration, what will there be left of the present-day civilisation of India? In Bengal alone, my blood has furnished them with their greatest philosopher, the greatest poet, the greatest historian, the greatest archaeologist, the greatest religious preacher; my blood has furnished India with the greatest of her modern scientists. These detractors ought to have known a little of our own history, and to have studied our three castes, and learnt that the Brahmin, the Kshatriya, and the Vaishya have equal right to be Sannyasins: the Traivarnikas have equal right to the Vedas. This is only by the way. I just refer to this, but I am not at all hurt if they call me a Shudra. It will be a little reparation for the tyranny of my ancestors over the poor.
Was Swami Vivekananda a Kshatriya?
It appears he was a kshatriya, or descended from Kshatriyas at least.