In Jainism there isn’t a canonical mantra specifically for buying a house. For auspicious beginnings, you can turn to prayers that seek the blessings of the Tirthankaras and right conduct rather than a house-specific chant.

What you can do:

• Recite the Navkar Mantra daily to invoke the blessings of Arihants, Siddhas, and the entire spiritual lineage.
• Offer a short, sincere bhavna (meditative intention) for peace, non-violence, and virtuous use of the new home.
• Pray to the Tirthankaras for a harmonious and safe living environment, and perform a simple, respectful consecration or puja if suited to your tradition.

If you’d like, I can share the authentic Navkar Mantra text and explain its meaning (different interpretations exist between Digambar and Shvetambar traditions). I can also point you to a JainKnowledge page with more details on Navkar Mantra.