Supplementing RSA-1024 with SHA-256 instead of SHA-1 won't cut it from a PCI-DSS compliance standpoint: RSA-2048 is a minimum for a large class of uses according to PCI-DSS's definition of
Strong Cryptography: Cryptography based on industry tested and accepted algorithms, along with key lengths that provide a minimum of 112-bits of effective key strength and proper key-management practices (..)
At the time of publication, examples of industry-tested and accepted standards and algorithms include AES (128 bits and higher), TDES/TDEA (triple-length keys), RSA (2048 bits and higher), ECC (224 bits and higher), and DSA/D-H (2048/224 bits and higher). See the current version of NIST Special Publication 800-57 Part 1 for more guidance on cryptographic key strengths and algorithms.
Note: The above examples are appropriate for persistent storage of cardholder data. The minimum cryptography requirements for transaction-based operations, as defined in PCI PIN and PTS, are more flexible as there are additional controls in place to reduce the level of exposure.
It is recommended that all new implementations use a minimum of 128-bits of effective key strength.
Also, just switching from SHA-1 to SHA-256 arguably would not help against real attacks: as a general rule, a security chain can only be as strong as its weakest link; and in many usage patterns, second-preimage (rather than collision) is what matters, making RSA-1024 a weaker link than SHA-1 is.
Addition following comment: SHA-1's collision resistance is weaker than RSA-1024. But in most applications, a successful attack requires breaking the hash's second preimage resistance, and SHA-1 remains extremely strong against that. There are a few exceptions where breaking collision resistance matters, like attacking an hypothetical certification authority still issuing SHA-1 based certificates and using predictable certificate numbers; but notice that from the standpoint a PCI-DSS entity, using a strong hash does not help protect from this hypothetical attack; what matters is that acceptors of certificates reject certificates made with SHA-1 (or reject certificates issued by authorities that do not have a policy stating that when they issue certificates based on SHA-1, they use an unpredictable certificate number).