Yes, individuals can perpetuate racism even when they do not intend to or are not consciously aware of it. This is known as implicit racism.
Implicit racism refers to unconscious biases, perceptions and prejudices ingrained in us about characteristics of different racial groups, regardless of our intent to not be racist. An example of an implicit racism can be as follows: When you watch the news and hear about an African-American getting arrested for physical violence you think "Not surprising since Black men are aggressive."