Generally yes, but there are two issues.
First, as pointed out by @NCperson , if the fence benefits only the business, it is a business expense, but if it benefits the entire house, then you allocate a portion of the expense to the business based on the percentage of the home that is used for business.
Second, not previously discussed, is that the fence is a capital improvement to the property, because it is permanently attached to the land. That means that the portion allocated to the business can only be expensed (deducted as an expense in the year paid for) if the cost is less than the $2500 safe harbor for expenses. More than that, and the fence is added to the property as an asset and depreciated over 40 years. That is, you deduct 1/40th the cost each year as long as you are in business.
[Edited to add; the depreciation time for a fence not used in an agricultural business is 15 years.]
[Edited to add: The fence does not qualify for section 179 depreciation, but may qualify for bonus depreciation, allowing you to deduct the cost faster than 15 years. If you enter the fence as a business asset, Turbotax will look at the cost and other factors and will tell you what kind of depreciation you qualify for.]
The portion allocated to the home (if any) is not deductible, but adds to the cost basis of the home, which may reduce the capital gains tax you owe when you sell.
Keep records of the depreciation of the business portion, because that also has to be accounted for when you sell the home. As does any depreciation on the home that you claim as a business expense. When you use your home for business, you need to keep those records of expenses and depreciation for as long as you own the home, plus 6 years after you sell.
