Although this question is already answered (tl;dr: yes, an empty href value is valid), none of the existing answers references the relevant specifications.
An empty string can’t be a URI. However, the href attribute doesn’t only take URIs as value, but also URI references. An empty string may be a URI reference.
HTML 4.01 uses RFC 2396, where it says in section 4.2. Same-document References (bold emphasis mine):
A URI reference that does not contain a URI is a reference to the current document. In other words, an empty URI reference within a document is interpreted as a reference to the start of that document, and a reference containing only a fragment identifier is a reference to the identified fragment of that document.
RFC 2396 is obsoleted by RFC 3986 (which is currently IETF’s URI standard), which essentially says the same.
HTML5 uses (valid URL potentially surrounded by spaces ? valid URL) W3C’s URL spec, which has been discontinued. WHATWG’s URL Standard should be used instead (see the last section).
HTML 5.1 uses (valid URL potentially surrounded by spaces ? valid URL) WHATWG’s URL Standard (see the next section).
WHATWG’s HTML uses (valid URL potentially surrounded by spaces) the definition of valid URL string from WHATWG’s URL Standard, where it says that it can be a relative-URL-with-fragment string, which must at least be a relative-URL string, which can be a path-relative-scheme-less-URL string, which is a path-relative-URL string that doesn’t start with a scheme string followed by :, and its definition says (bold emphasis mine):
A path-relative-URL string must be zero or more URL-path-segment strings, separated from each other by U+002F (/), and not start with U+002F (/).