I leased a residential care facility for business under a rent-to-own contract. I paid a deposit in the contract. Is the deposit considered as business expense?

No.  It might be considered a prepaid item, if first and last month of the lease is considered in the agreement, or it may be considered a receivable amount, such as deposit receivable.  It is not an expense until such time as it is forfeited, or paid in lieu of rent.