Caret is neither reserved nor "unreserved", which makes it an "unsafe character" in URLs. They should never appear in URLs unencoded. From RFC2396:
2.2. Reserved Characters
Many URI include components consisting of or delimited by, certain
special characters. These characters are called "reserved", since
their usage within the URI component is limited to their reserved
purpose. If the data for a URI component would conflict with the
reserved purpose, then the conflicting data must be escaped before
forming the URI.
reserved = ";" | "/" | "?" | ":" | "@" | "&" | "=" | "+" |
"$" | ","
The "reserved" syntax class above refers to those characters that are
allowed within a URI, but which may not be allowed within a
particular component of the generic URI syntax; they are used as
delimiters of the components described in Section 3.
Characters in the "reserved" set are not reserved in all contexts.
The set of characters actually reserved within any given URI
component is defined by that component. In general, a character is
reserved if the semantics of the URI changes if the character is
replaced with its escaped US-ASCII encoding.
2.3. Unreserved Characters
Data characters that are allowed in a URI but do not have a reserved
purpose are called unreserved. These include upper and lower case
letters, decimal digits, and a limited set of punctuation marks and
symbols.
unreserved = alphanum | mark
mark = "-" | "_" | "." | "!" | "~" | "*" | "'" | "(" | ")"
Unreserved characters can be escaped without changing the semantics
of the URI, but this should not be done unless the URI is being used
in a context that does not allow the unescaped character to appear.
2.4. Escape Sequences
Data must be escaped if it does not have a representation using an
unreserved character; this includes data that does not correspond to
a printable character of the US-ASCII coded character set, or that
corresponds to any US-ASCII character that is disallowed, as
explained below.