The short answer is maybe, but it is rare. It depends on each case. There is no right to have an attorney in divorce cases. If there is an extreme disparity in incomes where one spouse is the breadwinner and the other spouse earns little or no income, a court may grant a motion dictating the spouse with more money to pay for the court costs and provide funds for the other spouse's attorney.
What if I do have access to funds?
If a court determines you have enough funds to hire an attorney, they will likely not order your spouse to pay your fees, even if your spouse was the one to initiate the divorce.
The key here is the disparity in income between the two spouses. Sometimes a court will look to potential future funds that one may receive as an outcome of the divorce. This is known as an advancement. The court can grant that the attorney’s fees come out of your share of the assets in advance.