No. The Silent Phone application is not available under the GPL, the AGPL, or any other open source license.
As per the founder Phil Zimmerman;
"I’m a firm believer in publishing the source code for cryptographic software for peer review, to build public confidence that it contains no back doors, a tradition I started in 1991 with PGP. PGP is a proprietary product, even though the source code is available for peer review. Publishing the source code for peer review is not the same as making it available under an open source license.
Silent Phone has several major components, and not all of them are published under the same licensing terms. The entire body of source code for the complete Silent Phone client software is published for peer review purposes."