If you consider gifting people to brāhmaṇas as if they were one's property, as slavery, then both Rāma and Bharata engaged in slavery.
In Vālmīki Rāmāyaṇa (Ayodhyā kāṇḍa), Rāma instructs Lakṣmaṇa to gift slave-girls (dāsī's) to a brāhmaṇa:
kausalyām ca yāaśīrbhir bhaktaḥ paryupatiṣṭhati |
ācāryaḥ taittirīyāṇām abhirūpaḥ ca vedavit || 2-32-15
tasya yānam ...