There are a couple of different ways we can talk about the “genre” of a poem. The two main ways of classifying poetry are by its subject matter and by its form; often these are linked. For example, the psalm form often (but not always) is about religious or spiritual subject matter.
The first thing we can say about the form of the poem is that it is lyric: it uses prosody – the musical elements of language – to form stanzas and contains metrical feet, for example:
You may write | me down in | history
anapest | tribach | dactyl
With your bit | ter, twis | ted lies,
anapest | iamb | iamb
You may trod | me in the | very dirt
anapest | tribach | dactyl
But still | like dust | I'll rise.
iamb | iamb | iamb
The meter throughout does not follow the same pattern. Many lines are catalectic or hyper-catalectic: leaving off or adding syllables to lines. What this can tell us about a poem is that it was likely written to be spoken aloud, passionately, with dramatic pauses and to allow room for the reader to take breaths. You can see this if you watch Angelou read the poem: she stresses syllables and pauses for effect at certain points throughout the stanzas. Angelou’s first poetry collection, published in 1971, was principally poems which she had previously performed. “Still I Rise” was published in 1978, right before slam poetry came to be widely acknowledged, and so in addition to being a lyric poem, it could be considered a prototype slam poem.
Another element of this poem that we can analyae to figure out its genre is its subject matter and mood. The poem is written in the first person, the speaker uses the personal pronoun “I” and refers to an adversarial “you”. The poem deals with intense emotional and political issues like racism and sexism and contrasts these with playful, comedic, and sexual imagery and words. This contrast and the poem’s assertions of strength on the part of the speaker mean that this poem could also be considered an evolution of the confessional poetry that was popular in the USA in the 1950s and 1960s.
Taking all of these considerations into account, when we look at poems we use genre descriptively, not prescriptively. This means that it is not necessary, or even desirable, for every poem to adhere strictly to a set of rules to fit neatly into a genre. In this case, the poem “Still I Rise” can safely be classified as a lyric poem, and we can make arguments that it is also slam poetry and/or confessional poetry.
I have linked to a video of Angelou performing the poem, and to the Harvard poetry page which explains prosody terms like "anapest", "dactyl," and "iamb".