Certain payment products transfer the burden of PCI compliance to the payment services provider (Authorize.NET or Paypal Pro). However, they require that a consumer be forwarded to the payment provider's servers to complete their order. If your website integrates with Authorize.NET via an API then you are still liable for PCI compliance since your servers capture and transmit the credit card data first.
It is important for you to pay heed to requirement 3 of PCI-DSS guide, which is Protect Cardholder Data.
According to PCI-DSS https://www.pcisecuritystandards.org/documents/pci_dss_v2.pdf,
Unless you are an issuer or company that supports issuing services, Section 3.2 clearly explain that you cannot store sensitive data, even if encrypted.
However, if you are retaining sensitive data for normal course of business then you must have a defined data retention and disposal policy in place as explained in Section 3.1.
And you also must mask sensitive data when displayed according to Section 3.3
And you must render the stored sensitive data unreadable as explained in section 3.4
Edit:
By requirements 3.2 and sub requirement 3.2.1 mentioned in PCI-DSS document, I would like to iterate that
Sensitive data in storage/ transmission includes
1) Card Number
2) Card Holder name
3) Expiry Date
4) Service Code
Page 7 & 8 says, PAN defines the applicability of PCI-DSS.
IMO, Absence of FULL pan dissolves any PCI-DSS applicability. I agree with the answer above.
Hence, in this case PCI-DSS will not apply if you store any piece of this data along with first 6 and/or last 4 digits of the credit card number.