In the early time, sign language was often thought as iconic as in picture-like because of the earliest attitude toward signed language. Iconicity came with misconceptions. Any language in signing is not iconic, but it does have iconic words as in onomatopoeia found in spoken languages.
First, like spoken languages, many signed languages do have some onomatopoeic words. That is, many languages originated with onomatopoeia and evolved to some degree of abstraction in signed, spoken, and written forms.
The term onomatopoeia originated from late Latin and Greek meaning, "the making of a name or word (in imitation of a sound associated with the thing being named." The term "onama" means "word, name" and the "poiein" mean "to pose, make". There is no reference to sound in this word.
Hence, I will use these interchangeable terms onomatopoeia and iconicity for both signed and spoken languages in general. Otherwise, to be specific, I would coin the terms phonomatopoeia for vocal-auditory iconicity and visonomatopoeia (or formerly thought of manonotopoeia for visual-spatial iconicity.
Onomatopoeia is found in all languages from Chinese writing to spoken and signed languages especially in the earliest emergence and evolution of language.
Myth: What words (whether spoken or signed) look like or sound like are similar to the objects or sounds in real life.
In fact, onomatopoeic words (signed or spoken) for the same objects or sounds are different across languages (spoken or signed). For example, "meow" in English, "miau" in Finnish, and so on. Likewise, there are different onomatopoeic symbols for "tree" across signed languages.
Fact: If spoken or signed words were iconic (whether in sound or visue), foreigners would be able to understand without learning.
Fact: Iconic words in ASL are often unrecognizable by a nonsigner who is not told what their meanings are in the first place. They become iconic usually after non-signers are told what they mean.
In a study, a group of hearing people, who didn't know ASL, cannot identify 10 iconic ASL words. Nil. Next, the group was provided a list of words with mulitple choices for each. They got about a small percent right. When they were given an answer, they would think they already knew before. But, the truth is that they wouldn't know in the first pleace regardless of the iconic words.
Moreover, a brain science study shows that iconic ASL words and gestures are processed in different regions of the brain.
Myth: Many "teachers" in "baby sign language" business teach that many signs (e.g. "eat", "milk", etc) taught to hearing babies are iconic and are easy to learn (because they are iconic).
Fact: Research shows that iconicity does not play a role in the acquisition of ASL by infants and children. For example, a child learns the sign milk but she/he has no idea how milk is obtained from a cow.
Furthermore, a favorite evidence is that ASL-speaking toddlers don't acquire the ASL pronouns (extremely iconic) till the same timeline as in spoken language (at about 18-20 months).
In relation to this, gestural pointing in babies (regardless signing or not) emerge at about 9 months but the same form of pointing for pronouns in ASL emerge at 18-20 months which is the same timeline for pronouns in spoken language. Remember that the linguistic portion of the brain function independently from signing or speech. It only recognizes languages in both signing and speech.
In summary, all languages whether signed or spoken have some iconic or onomatopoeic symbols/words/morphemes that are not necessarily understood by foreigners.
[Posted, 2011, updated 2019]
You may be interested in Gesture vs Word what the brain tells.