Speech representations learned from Self-supervised learning (SSL) models can benefit various speech processing tasks. However, utilizing SSL representations usually requires fine-tuning the pre-trained models or designing task-specific downstream models and loss functions, causing much memory usage and human labor. Recently, prompting in Natural Language Processing (NLP) has been found to be an efficient technique to leverage pre-trained language models (LMs). Specifically, prompt tuning optimizes a limited number of task-specific parameters with a fixed pre-trained model; as a result, only a small set of parameters is needed to be stored for each task. Prompt tuning improves computation and memory efficiency by leveraging the pre-trained LM's prediction ability. Nevertheless, such a paradigm is little studied in the speech community. We report in this paper the first exploration of the prompt tuning paradigm for speech processing tasks based on Generative Spoken Language Model (GSLM). Experiment results show that the prompt tuning technique achieves competitive performance in speech classification tasks with fewer trainable parameters than fine-tuning specialized downstream models. We further study the technique in challenging sequence generation tasks. Prompt tuning also demonstrates its potential, while the limitation and possible research directions are discussed in this paper. The source code is available on https://github.com/ga642381/SpeechPrompt.