The Mahabharata war has been given a date of around 3300 BC by back-tracing planetary positions from scriptural references (archeo-astronomy). The Ramayana is speculated to be anywhere between a few generations prior to the Mahabharata to a few millennia before. But is there any reference in the Puranas that affirms that both these stories happened in the current Yuga cycle we are living in? Because, do planetary positions repeat themselves in each Yuga cycle?
Yes, both the Ramayana and the Mahabharata happened in the present Vaivasvata Manvantara.. Let me address each one separately. Keep in mind that we're currently living in the 28th Kali Yuga of the Vaivasvata Manvantara.
Ramayana: Here is what the Matysa Purana says, while enumerating various incarnations of Vishnu in the Vaivasvata Manvantara in chronological order:
In the 24th Treta Yuga, the seventh manifestation was that of Sri Ramchandra, as the son of Dasharatha, and with Vasishta as the priest, to kill Ravana.
Mahabharata: This excerpt from the Shatarudra Samhita of the Shiva Purana, in the course of describing the various Dwapara Yugas of the Vaivasvata Manvantara, says this about Krishna:
In the twenty-eighth aeon of Dwapara, there will be Dwaipayana Vyasa, the son of Parashara, and the most excellent of Purushas [Vishnu] shall be born as Krishna with his one-sixth part, as the foremost of the sons of Vasudeva.
By the way, the Shiva Purana excerpt I linked to also describes an incarnation of Shiva named Lakulisha, whom I discuss here.