American Express Membership Rewards is Delta's only major credit card transfer partner and points earned in the program can be converted to Delta SkyMiles at a 1:1 ratio.
Conversion Rate & Fees
Membership Rewards Points can be transferred to Delta SkyMiles at a 1:1 ratio. This means that 1,000 AMEX Points can be converted to 1,000 Delta SkyMiles.
Transfers must be done in 1,000-point increments and you must have at least 1,000 AMEX Points to initiate a transfer.

Fees
Every time you transfer AMEX Points to a U.S. airline frequent flyer program, you will be charged an Excise Tax Offset of $0.0006 per point. This comes out to being $0.60 per 1,000 AMEX Points you transfer.
AMEX allows you to pay for the fee either in points or with an eligible Membership Rewards credit cards connected to the account. When paying in points, they will be worth 0.5 cents each which is a bad redemption value considering you can easily get 1 cent redeeming directly with AMEX or higher when transferring to partners (such as Delta).

I highly suggest paying with your credit card when transferring points.
Conversion Calculator
Use the Conversion Calculator to calculate the transfer of American Express Membership Rewards Points to Delta SkyMiles.
Excise Tax Offset fee for this transfer: $0.00
Other Ways To Earn SkyMiles
Outside of transferring Membership Rewards points to Delta, you can also earn lots of SkyMiles using Delta's co-branded credit cards. They offer a whopping seven credit cards that you can use to earn SkyMiles via everyday spending and intro bonuses.
These cards also offer fantastic benefits including free checked bags, annual companion passes in which someone can fly with you for just the cost of taxes and fees, and the ability to spend your way to higher Delta Medallion Status.
If you fly Delta frequently, you'll want to consider picking up at least one of their co-branded credit cards.
FAQ
How many AMEX Points equals Delta SkyMiles when transferred?
Transferring 1 AMEX Membership Rewards Point will give you 1 Delta SkyMile.
How long does it take for AMEX Points to transfer to Delta?
It typically only takes a few minutes to be reflected in your SkyMiles account, but could take up to 24 hours.
How much does it cost to transfer AMEX Points to Delta SkyMiles?
AMEX will charge you $0.0006 per point transferred to Delta SkyMiles. This means that every 1,000 points you transfer will cost you $0.60.