Even though the federal statute is named the Investment Advisers Act of 1940, persons regulated by that act often refer to themselves as "advisors" and not "advisers". Which is spelling is correct?
In English, we use both the -er and -or as endings to create agent-nouns. For example, the verb "create" becomes the agent-noun "creator". The question remains, however, which ending should be used. In general, the -or ending is used with verbs that have Latin language origins. This is most prevalent when the English verb is derived from the supine form of a Latin verb. In Latin, the supine is a verbal noun. For example, the supine of dicto, meaning to speak or declare, is dictatum, from which the English verb "dictate" is formed. The agent-noun of "dictate" is "dictator". Agent nouns formed from non Latin verbs are often formed with the suffix -er. For example, "make" is derived from the Old English macian and the agent noun of "make", is "maker".
The verb "advise" is from the Old French. This supports the view that the verbal noun should be "adviser". Reaching farther back, however, "advise" is derived from the Latin verb visus (the past participle of video, meaning to see). In addition, the adjectival form of the word is "advisory". Both of these facts favor the Latinate form of "advisor". Thus, it should come as no surprise that both forms are common.
The California Corporate Securities Law of 1968 follows the federal act by using "adviser". Cal. Corp. Code § 25009. However, the California legislature has not been entirely consistent. Several other statutes adopt the -or form. Section 19805 of the Business and Professions Code even refers to investment advisors under the Investment Advisors Act of 1940.
The bottom line is that "adviser" and "advisor" are equally acceptable. Congress chose the English form (-er), but the choice is yours (unless you are intending to refer to the statute or the statutory term).