On a loan to purchase an investment rental property - yes, points (sometimes called loan origination fees or discount points) are tax deductible but not as a whole in the year the property is purchased.
Points are treated as prepaid interest so even though these fees are paid up front they have to be deducted as an expense over the life of the loan. As an example, if you borrowed $200,000 with a 30 year mortgage and paid 2 points then you paid $4,000 in points. Each year you would have $133 ($4000 / 30 = $133.33) in deductible interest expense (in addition to your normal interest you pay every month on the loan) except for the first and last year. For example, if you bought the property in June then the first year you'd have half the $133 available as your interest expense write-off, etc. The last year you would have whatever the remainder is.
If you sell the property and the loan is paid off or you refinance before the loan term is due then whatever points expense is left from your annual $133 deduction (in our example) would be an interest expense tax deduction in that year. If you refinanced in the third year and the month you got the original loan was June then you'd have $67 the first year, $133 the second year, and $3800 the third year when you refinanced out of the loan ($4000 - $67(year one) - $133(year two) = $3800 left).
Keep in mind that this is another area where tax deductions are different than what they are on your personal residence. The bottom line, obviously, is that paying points on a loan for an investment property is something you generally want to avoid or at least limit.
Lastly, as there are more than one type of fees you could be paying when getting a loan you certainly want to look at this carefully. Generally the fee referenced here will be on line 801 of your closing statement for the property (HUD-1). Having a qualified tax professional look this over is a good idea!