Yes, the caste system is discussed in many places in the Bhagavad Gita. First of all, Arjuna discusses the consequences of Varnashankara or caste-mixing in Chapter 1:
With the destruction of the dynasty, the eternal family tradition is vanquished, and thus the rest of the family becomes involved in irreligion. When irreligion is prominent in the family, O Kṛṣṇa, the women of the family become polluted, and from the degradation of womanhood, O descendant of Vṛṣṇi, comes unwanted progeny. An increase of unwanted population certainly causes hellish life both for the family and for those who destroy the family tradition. The ancestors of such corrupt families fall down, because the performances for offering them food and water are entirely stopped. By the evil deeds of those who destroy the family tradition and thus give rise to unwanted children, all kinds of community projects and family welfare activities are devastated. O Kṛṣṇa, maintainer of the people, I have heard by disciplic succession that those whose family traditions are destroyed dwell always in hell.
Then in Chapter 2, Krishna discusses the importance of Arjuna doing his Dharma as a Kshatriya:
Considering your speciﬁc duty as a kṣatriya, you should know that there is no better engagement for you than ﬁghting on religious principles; and so there is no need for hesitation. O Pārtha, happy are the kṣatriyas to whom such ﬁghting opportunities come unsought, opening for them the doors of the heavenly planets. If, however, you do not perform your religious duty of ﬁghting, then you will certainly incur sins for neglecting your duties and thus lose your reputation as a ﬁghter.
And in Chapter 3 Krishna stresses the importance of doing one's one Dharma rather than someone else's Dharma:
It is far better to discharge one’s prescribed duties, even though faultily, than another’s duties perfectly. Destruction in the course of performing one’s own duty is better than engaging in another’s duties, for to follow another’s path is dangerous.
And in Chapter 4 Krishna discusses how the caste system was created by him:
According to the three modes of material nature and the work associated with them, the four divisions of human society are created by Me. And although I am the creator of this system, you should know that I am yet the nondoer, being unchangeable.
Chapter 5 contains an important statement about how regardless of whether people have differences in bodies based on caste, species, etc., the soul remains the same, and how the wise recognize everyone's soul as having the same essential nature:
The humble sages, by virtue of true knowledge, see with equal vision a learned and gentle brāhmaṇa, a cow, an elephant, a dog and a dog-eater.
I could go on, but perhaps the most important Gita statement related to caste is in Chapter 9:
O son of Pṛthā, those who take shelter in Me, though they be of lower birth – women, vaiśyas and śūdras – can attain the supreme destination.
That is referring to Sharanagati or complete surrender to Vishnu, as Vedanta Desikan discusses in this chapter of the Rahasyatraya Sara.