Time series forecasting aims to model temporal dependencies among variables for future state inference, holding significant importance and widespread applications in real-world scenarios. Although deep learning-based methods have achieved remarkable progress, they still exhibit suboptimal performance in long-term forecasting. Recent research demonstrates that large language models (LLMs) achieve promising performance in time series forecasting, but this progress is still met with skepticism about whether LLMs are truly useful for this task. To address this, we propose Time-Prompt, a framework for activating LLMs for time series forecasting. Specifically, we first construct a unified prompt paradigm with learnable soft prompts to guide the LLM's behavior and textualized hard prompts to enhance the time series representations. Second, to enhance LLM' comprehensive understanding of the forecasting task, we design a semantic space embedding and cross-modal alignment module to achieve fusion of temporal and textual data. Finally, we efficiently fine-tune the LLM's parameters using time series data. Furthermore, we focus on carbon emissions, aiming to provide a modest contribution to global carbon neutrality. Comprehensive evaluations on 6 public datasets and 3 carbon emission datasets demonstrate that Time-Prompt is a powerful framework for time series forecasting.